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en-us2014 Maplesoft, A Division of Waterloo Maple Inc.Maplesoft Document SystemSun, 20 Apr 2014 13:38:52 GMTSun, 20 Apr 2014 13:38:52 GMTThe most recent questions and posts on MaplePrimes tagged with equationshttp://www.mapleprimes.com/images/mapleprimeswhite.jpgMaplePrimes - Questions and Posts tagged with equations
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Getting a system of linear equations out of matrices
http://www.mapleprimes.com/questions/201410-Getting-A-System-Of-Linear-Equations?ref=Feed:MaplePrimes:Tagged With equations
<p>Hey Guys<br><br>I'm designing some stuff for controll theory</p>
<p>There I met following problem:</p>
<p>I want calculate the matrix A which is the product of X and G.</p>
<p>A is 6x6 matrix and all values in the diagonal are ones, the rest is undefined and should be calculated</p>
<p>X is 6x6 diagonal matrix with the values X1...X6</p>
<p>and G is also 6x6 and have all these values.</p>
<p> </p>
<p>now I'm stuck 'cause I haven't used Maple frequently (only some simple stuff up to now, nothing with matrices)</p>
<p>I'd really appreciate it, if someone can tell how to tackle this problem</p>
<p>Cheers</p><p>Hey Guys<br /><br />I'm designing some stuff for controll theory</p>
<p>There I met following problem:</p>
<p>I want calculate the matrix A which is the product of X and G.</p>
<p>A is 6x6 matrix and all values in the diagonal are ones, the rest is undefined and should be calculated</p>
<p>X is 6x6 diagonal matrix with the values X1...X6</p>
<p>and G is also 6x6 and have all these values.</p>
<p> </p>
<p>now I'm stuck 'cause I haven't used Maple frequently (only some simple stuff up to now, nothing with matrices)</p>
<p>I'd really appreciate it, if someone can tell how to tackle this problem</p>
<p>Cheers</p>201410Thu, 17 Apr 2014 06:30:22 ZKinkillaKinkillahow to solve a set of equations for a ratio in terms of variables involved?
http://www.mapleprimes.com/questions/201319-How-To-Solve-A-Set-Of-Equations-For?ref=Feed:MaplePrimes:Tagged With equations
<p>This is better explained with simple example. Suppose I have these 2 equations</p>
<p>a:='a';b:='b';x:='x';<br>eqs:=[3*a+4*b = 3*x, 5*a+7*b = 7*x];</p>
<p>What I want is to solve for (a/x) and (b/x) from the above, and not for "a" and "b".</p>
<p>Currently, I do this manually as follows. First divide both equations by 'x' to obtain the ratio. I had to do this manually as writing eqs/x gave expression which was hard to work with for what I want to do. I could not simplify it for what I wanted. So I typed this</p>
<p>eqs2:=[3*(a/x)+4*(b/x)=3,5*(a/x)+7*(b/x)=7]; %manually typed !</p>
<p>Now used algsubs to replace (a/x) by new variable z1, and replace (b/x) by new variable z2, then solve for z1,z2 (btw, I had to do algsubs one at a time. (need to look at this later, but not impotant)</p>
<p>algsubs(a/x=z1,eqs2);<br>algsubs(b/x=z2,%);<br>solve(%,{z1,z2});</p>
<p> {z1=-7,z2=6}</p>
<p>Is there a way or function(s) to automate this. The hard part is telling Maple to use the ratio as new variable starting from set of equations.</p><p>This is better explained with simple example. Suppose I have these 2 equations</p>
<p>a:='a';b:='b';x:='x';<br>eqs:=[3*a+4*b = 3*x, 5*a+7*b = 7*x];</p>
<p>What I want is to solve for (a/x) and (b/x) from the above, and not for "a" and "b".</p>
<p>Currently, I do this manually as follows. First divide both equations by 'x' to obtain the ratio. I had to do this manually as writing eqs/x gave expression which was hard to work with for what I want to do. I could not simplify it for what I wanted. So I typed this</p>
<p>eqs2:=[3*(a/x)+4*(b/x)=3,5*(a/x)+7*(b/x)=7]; %manually typed !</p>
<p>Now used algsubs to replace (a/x) by new variable z1, and replace (b/x) by new variable z2, then solve for z1,z2 (btw, I had to do algsubs one at a time. (need to look at this later, but not impotant)</p>
<p>algsubs(a/x=z1,eqs2);<br>algsubs(b/x=z2,%);<br>solve(%,{z1,z2});</p>
<p> {z1=-7,z2=6}</p>
<p>Is there a way or function(s) to automate this. The hard part is telling Maple to use the ratio as new variable starting from set of equations.</p>201319Sun, 06 Apr 2014 17:49:16 Znmnmcomparison numerical and analytic
http://www.mapleprimes.com/questions/201317-Comparison-Numerical-And-Analytic?ref=Feed:MaplePrimes:Tagged With equations
<p>Dear all;</p>
<p>Please how can I plot the error between the two function. </p>
<p> </p><p>Dear all;</p>
<p>Please how can I plot the error between the two function. </p>
<p> </p>201317Sun, 06 Apr 2014 02:06:59 ZsarrasarraA command like fmincon command(matlab) in maple
http://www.mapleprimes.com/questions/201271-A-Command-Like-Fmincon-Commandmatlab-In-Maple?ref=Feed:MaplePrimes:Tagged With equations
<p>Hi all</p>
<p>In matlab software we have a command namely fmincon which minimizes any linear/nonlinear algebric equations subject to linear/nonlinear constraints.</p>
<p>Now my question is that: what is the same command in maple?or how can we minimize linear/nonlinear function subject to linear/nonlinear constraints in maple?</p>
<p>thanks a lot</p>
<!--break-->
<p>Mahmood Dadkhah</p>
<p>Ph.D Candidate</p>
<p>Applied Mathematics Department</p><p>Hi all</p>
<p>In matlab software we have a command namely fmincon which minimizes any linear/nonlinear algebric equations subject to linear/nonlinear constraints.</p>
<p>Now my question is that: what is the same command in maple?or how can we minimize linear/nonlinear function subject to linear/nonlinear constraints in maple?</p>
<p>thanks a lot</p>
<!--break-->
<p>Mahmood Dadkhah</p>
<p>Ph.D Candidate</p>
<p>Applied Mathematics Department</p>201271Sun, 30 Mar 2014 20:40:18 Zmahmood180mahmood180How do I solve a system of equations in Maple 17 for Mac?
http://www.mapleprimes.com/questions/201258-How-Do-I-Solve-A-System-Of-Equations?ref=Feed:MaplePrimes:Tagged With equations
<p>I was required to purchase Maple 17 for my upcoming Calculus III course, and until now, I have been using my TI-Nspire CAS CX for all of my CAS needs. I am going through various tutorials/labs in an effort to learn how to use the Maple 17 Software. As a part of this process, I am attempting to solve a system of equations and was told to use the following command:</p>
<p>>solve({2*x+3*y=7,5*x+8*y=9},{x,y}); </p>
<p>in order to receive the answer </p>
<p>{y=-17,x=29}.</p>
<p> </p>
<p>Instead, I have received the following error message, which has no help attached to it through the help page.</p>
<p>solve({2*x+3*y = 7, 5*x+8*y = 9}, {x, y});<br>Warning, solving for expressions other than names or functions is not recommended.</p>
<p>I am hoping this has something to do with Mac vs. Windows software, and that it has a simple solution. I would greatly appreciate any guidance!</p><p>I was required to purchase Maple 17 for my upcoming Calculus III course, and until now, I have been using my TI-Nspire CAS CX for all of my CAS needs. I am going through various tutorials/labs in an effort to learn how to use the Maple 17 Software. As a part of this process, I am attempting to solve a system of equations and was told to use the following command:</p>
<p>>solve({2*x+3*y=7,5*x+8*y=9},{x,y}); </p>
<p>in order to receive the answer </p>
<p>{y=-17,x=29}.</p>
<p> </p>
<p>Instead, I have received the following error message, which has no help attached to it through the help page.</p>
<p>solve({2*x+3*y = 7, 5*x+8*y = 9}, {x, y});<br />Warning, solving for expressions other than names or functions is not recommended.</p>
<p>I am hoping this has something to do with Mac vs. Windows software, and that it has a simple solution. I would greatly appreciate any guidance!</p>201258Sat, 29 Mar 2014 14:53:26 ZebetwalshebetwalshPlot numerical solution
http://www.mapleprimes.com/questions/201242-Plot-Numerical-Solution-?ref=Feed:MaplePrimes:Tagged With equations
<p>Dear all;</p>
<p>Please give me few minutes to correct the output of this procedure.Many thinks. <br> We will solve the waves equations: diff(f(x,y,t),t$2)=c^2*( diff(f(x,y,t),x$2) +diff(f(x,y,t),y$2)); where (x,y,t) in [0,1]*[0,1]*[0,T] using finite difference. With Initial boundary conditions: [u(0,y,t)=u(1,y,t)=0], [u(x,0,t)=u(x,1,t)=0], [u(x,y,0)=f(x,y), diff(u(x,y,0),t)=g(x,y)]... The code is done and perfect but....The output of this procedure is Nothing. How can I plot the solution...<br><br>f:=(x,y)->x*(x-1)*y*(y-1);<br>g:=(x,y)->0;<br>analytical_sol:=proc(dx,dy,dt,Tf)<br>local Ft, Fx,Fy,x,y, c1,c2,c,j,k,i,u;<br>Ft := floor(Tf/dt)+1;<br>Fx := floor(1/dx)+1;<br>Fy := floor(1/dy)+1;<br>x:=[seq(0..1,dx)]:<br>y:=[seq(0..1,dy)]:<br>c1 := (c*dt/dx)^2; <br>c2 := (c*dt/dy)^2;<br>#Initial position<br>for j from 1 to Fx do <br> for k from 1 to Fy do <br> u[j,k,1] := f(-dx + j*dx, -dy + k*dy) -dt*g(-dx+j*dx, -dy + k*dy);<br> u[j,k,2] := f(-dx + j*dx, -dy +k*dy);<br>end do;<br>end do;<br><br># Boundary values j=1<br>for i from 1 to Ft +1 do <br> for k from 1 to Fy do <br> u[1,k,i] := 0;<br> end do;<br> for k from 1 to Fy do <br> u[Fx,k,i] := 0;<br> end do;<br><br> for j from 1 to Fx do <br> u[j,1,i] := 0;<br> end do;<br> <br> for j from 1 to Fx do <br> u[j,Fy,i] := 0;<br> end do;<br>end do;<br><br>for i from 3 to Ft + 1 do <br> for j from 2 to Fx-1 do<br> for k from 2 to Fy-1 do<br>u[j, k, i] := 2*u[j,k,i-1] - u[j,k,i-2] + c1*(u[j+1,k,i-1]-2*u[j,k,i-1]+u[j-1,k,i-1]) + c2*(u[j,k+1,i-1] - 2*u[j, k, i-1] + u[j,k-1, i-1]);<br>end do;<br>end do;<br>end do;<br>return Matrix([seq([seq([seq(u[i,j,k],i=1..Fx)],j=1..Fy)],k=1..Ft)]):<br>end proc:</p>
<p>## Try the test<br>f:=(x, y) -> x (x - 1) y (y - 1)<br>g:=(x, y) -> 0;<br>analytical_sol(0.1,0.1,0.1,2);<br> <br><br></p><p>Dear all;</p>
<p>Please give me few minutes to correct the output of this procedure.Many thinks. <br /> We will solve the waves equations: diff(f(x,y,t),t$2)=c^2*( diff(f(x,y,t),x$2) +diff(f(x,y,t),y$2)); where (x,y,t) in [0,1]*[0,1]*[0,T] using finite difference. With Initial boundary conditions: [u(0,y,t)=u(1,y,t)=0], [u(x,0,t)=u(x,1,t)=0], [u(x,y,0)=f(x,y), diff(u(x,y,0),t)=g(x,y)]... The code is done and perfect but....The output of this procedure is Nothing. How can I plot the solution...<br /><br />f:=(x,y)->x*(x-1)*y*(y-1);<br />g:=(x,y)->0;<br />analytical_sol:=proc(dx,dy,dt,Tf)<br />local Ft, Fx,Fy,x,y, c1,c2,c,j,k,i,u;<br />Ft := floor(Tf/dt)+1;<br />Fx := floor(1/dx)+1;<br />Fy := floor(1/dy)+1;<br />x:=[seq(0..1,dx)]:<br />y:=[seq(0..1,dy)]:<br />c1 := (c*dt/dx)^2; <br />c2 := (c*dt/dy)^2;<br />#Initial position<br />for j from 1 to Fx do <br /> for k from 1 to Fy do <br /> u[j,k,1] := f(-dx + j*dx, -dy + k*dy) -dt*g(-dx+j*dx, -dy + k*dy);<br /> u[j,k,2] := f(-dx + j*dx, -dy +k*dy);<br />end do;<br />end do;<br /><br /># Boundary values j=1<br />for i from 1 to Ft +1 do <br /> for k from 1 to Fy do <br /> u[1,k,i] := 0;<br /> end do;<br /> for k from 1 to Fy do <br /> u[Fx,k,i] := 0;<br /> end do;<br /><br /> for j from 1 to Fx do <br /> u[j,1,i] := 0;<br /> end do;<br /> <br /> for j from 1 to Fx do <br /> u[j,Fy,i] := 0;<br /> end do;<br />end do;<br /><br />for i from 3 to Ft + 1 do <br /> for j from 2 to Fx-1 do<br /> for k from 2 to Fy-1 do<br />u[j, k, i] := 2*u[j,k,i-1] - u[j,k,i-2] + c1*(u[j+1,k,i-1]-2*u[j,k,i-1]+u[j-1,k,i-1]) + c2*(u[j,k+1,i-1] - 2*u[j, k, i-1] + u[j,k-1, i-1]);<br />end do;<br />end do;<br />end do;<br />return Matrix([seq([seq([seq(u[i,j,k],i=1..Fx)],j=1..Fy)],k=1..Ft)]):<br />end proc:</p>
<p>## Try the test<br />f:=(x, y) -> x (x - 1) y (y - 1)<br />g:=(x, y) -> 0;<br />analytical_sol(0.1,0.1,0.1,2);<br /> <br /><br /></p>201242Wed, 26 Mar 2014 23:28:16 ZsarrasarraHFloat Error solving partial differential equations
http://www.mapleprimes.com/questions/201235-HFloat-Error-Solving-Partial-Differential?ref=Feed:MaplePrimes:Tagged With equations
<p>When trying to solve a set of partial differential equations, I always get the following error. I don't know what it means. Can somebody help me?</p>
<p> </p>
<p><img src="/view.aspx?sf=201235_question/Capture.PNG" alt=""></p><p>When trying to solve a set of partial differential equations, I always get the following error. I don't know what it means. Can somebody help me?</p>
<p> </p>
<p><img src="/view.aspx?sf=201235_question/Capture.PNG" alt=""></p>201235Wed, 26 Mar 2014 09:56:26 ZnismitsnismitsDifferential Equations - Quasi Period
http://www.mapleprimes.com/questions/201191-Differential-Equations--Quasi-Period?ref=Feed:MaplePrimes:Tagged With equations
<p class="p1">Hi, can I get some help with this?</p>
<p class="p1"><br>The question is:</p>
<p class="p1">Consider the following IVP for a mass of m = 2 kg attached to a spring with a spring constant k = 9 N/m. The spring mass system is in a medium with damping constant b.</p>
<p class="p1">2y" + by' + 9y = 0</p>
<p class="p1">y(0) = 0, D(y)(0) = -3 </p>
<p class="p1"> </p>
<p class="p1">It then asks find three values b1, b2, b3 where b1 is underdamped, b2 is critical, b3 is over. </p>
<p class="p1">I set b1 as 1, b2 as sqt 72, b3 as 9. </p>
<p class="p1"> </p>
<p class="p1">Then it asks to find the quasi period. </p>
<p class="p1">I can't get my quasi period right. My answer is 2pi/ sqrt (4.5).</p>
<p class="p1"> </p>
<p class="p1">Any help? </p><p class="p1">Hi, can I get some help with this?</p>
<p class="p1"><br />The question is:</p>
<p class="p1">Consider the following IVP for a mass of m = 2 kg attached to a spring with a spring constant k = 9 N/m. The spring mass system is in a medium with damping constant b.</p>
<p class="p1">2y" + by' + 9y = 0</p>
<p class="p1">y(0) = 0, D(y)(0) = -3 </p>
<p class="p1"> </p>
<p class="p1">It then asks find three values b1, b2, b3 where b1 is underdamped, b2 is critical, b3 is over. </p>
<p class="p1">I set b1 as 1, b2 as sqt 72, b3 as 9. </p>
<p class="p1"> </p>
<p class="p1">Then it asks to find the quasi period. </p>
<p class="p1">I can't get my quasi period right. My answer is 2pi/ sqrt (4.5).</p>
<p class="p1"> </p>
<p class="p1">Any help? </p>201191Fri, 21 Mar 2014 03:41:04 ZSill KongSill Kongproblem with system of ode's or maple ?
http://www.mapleprimes.com/questions/201177-Problem-With-System-Of-Odes-Or-Maple-?ref=Feed:MaplePrimes:Tagged With equations
<p>hi all.<br>i have a system of ODE's including 9 set of coupled OED's . </p>
<p>i have converted second deravaties to dd2 , in other words : diff(a[i](t),t,t)=dd2[i](t) . i =1..9 :</p>
<p>and i have set these 9 equations in form of vibrational equations such : (M.V22)[i]+(K(t).V(t))[i]+P(t)[i] = eq[i] , where M is coefficient Matrix of second derivatives , V22 is Vector of second derivaties , for example V22[1] = diff(a[1](t),t,t) , and P(t) is the numeric part of equations ( they are pure number and do not contain any symbolic function ) and K(t).V(t) is the remaining part of equations such that : (K(t).V(t))[i] = eq[i] - (M.V22)[i] - P(t)[i] , and V(t) are vector of a[i](t)'s which V(t)[1] = a[1](t) ,<br><br>i have used step by step time integration method (of an ebook which i have attachted that part of ebook here), when i set time step of solving process to h=0.01 , i can solve this system up to time one second or more, but when i choose h=0.001 or smaller, the answer diverges after 350 steps . i do not know whether the problem is in my ODS system, or maple can not handle this <a href='http://www.maplesoft.com/support/help/search.aspx?term=the' target='_new'>?the</a> answer about the time t=0.3 are the same in both steps, but after that, the one with stpe time h=0.001 diverges. my friend has solved this in mathematica without any problem, could any body help me ?! it is urgent for me to solve this problem,thnx everybody.<br><br><br><a href="/view.aspx?sf=201177_question/ebook.pdf">ebook.pdf</a> <a href="/view.aspx?sf=201177_question/step_=_0.001.mw">step_=_0.001.mw</a> <a href="/view.aspx?sf=201177_question/step_=_0.01.mw">step_=_0.01.mw</a> </p><p>hi all.<br>i have a system of ODE's including 9 set of coupled OED's . </p>
<p>i have converted second deravaties to dd2 , in other words : diff(a[i](t),t,t)=dd2[i](t) . i =1..9 :</p>
<p>and i have set these 9 equations in form of vibrational equations such : (M.V22)[i]+(K(t).V(t))[i]+P(t)[i] = eq[i] , where M is coefficient Matrix of second derivatives , V22 is Vector of second derivaties , for example V22[1] = diff(a[1](t),t,t) , and P(t) is the numeric part of equations ( they are pure number and do not contain any symbolic function ) and K(t).V(t) is the remaining part of equations such that : (K(t).V(t))[i] = eq[i] - (M.V22)[i] - P(t)[i] , and V(t) are vector of a[i](t)'s which V(t)[1] = a[1](t) ,<br><br>i have used step by step time integration method (of an ebook which i have attachted that part of ebook here), when i set time step of solving process to h=0.01 , i can solve this system up to time one second or more, but when i choose h=0.001 or smaller, the answer diverges after 350 steps . i do not know whether the problem is in my ODS system, or maple can not handle this ?the answer about the time t=0.3 are the same in both steps, but after that, the one with stpe time h=0.001 diverges. my friend has solved this in mathematica without any problem, could any body help me ?! it is urgent for me to solve this problem,thnx everybody.<br><br><br><a href="/view.aspx?sf=201177_question/ebook.pdf">ebook.pdf</a> <a href="/view.aspx?sf=201177_question/step_=_0.001.mw">step_=_0.001.mw</a> <a href="/view.aspx?sf=201177_question/step_=_0.01.mw">step_=_0.01.mw</a> </p>201177Wed, 19 Mar 2014 18:09:24 Zmehdi jafarimehdi jafariError, (in dsolve) invalid arguments; expected an equation, or a set or list of them, received...
http://www.mapleprimes.com/questions/201152-Error-in-Dsolve-Invalid-Arguments?ref=Feed:MaplePrimes:Tagged With equations
<p>b := 1;</p>
<p>h := 1;</p>
<p>A := b*h;</p>
<p>E := 210*10^9;</p>
<p>qr := 100;</p>
<p>Dp := (1/12)*E*b*h^3;</p>
<p>R := 20;</p>
<p>teta := 3;</p>
<p>sys1 := {(E.A+Dp/R^2)*(diff(u(t), `$`(t, 2))) = -E*A*(diff(w(t), t))/R+Dp*(diff(w(t), `$`(t, 3)))/R, -Dp*(diff(w(t), `$`(t, 4))) = E*A*(diff(u(t), t))/R-Dp*(diff(u(t), `$`(t, 3)))/R+E*A/R-100};</p>
<p>dsolve(sys1);</p>
<p>#THİS GAVE ME THE RESULTS LİKE THAT:</p>
<p>{u(t) = (1/4801)*_C3*(-1+sqrt(4801))^(3/2)*exp(-(1/20)*sqrt(-1+sqrt(4801))*t)-(1/4801)*_C4*(-1+sqrt(4801))^(3/2)*exp((1/20)*sqrt(-1+sqrt(4801))*t)-(1/4801*I)*_C5*(1+sqrt(4801))^(3/2)*exp(-(1/20*I)*sqrt(1+sqrt(4801))*t)-(1/4801)*_C6*(-1+sqrt(4801))^(3/2)*exp((1/20)*sqrt(-1+sqrt(4801))*t)+(1/4801)*_C3*sqrt(-1+sqrt(4801))*exp(-(1/20)*sqrt(-1+sqrt(4801))*t)-(1/4801)*_C4*sqrt(-1+sqrt(4801))*exp((1/20)*sqrt(-1+sqrt(4801))*t)+(1/4801*I)*_C5*sqrt(1+sqrt(4801))*exp(-(1/20*I)*sqrt(1+sqrt(4801))*t)-(1/4801)*_C6*sqrt(-1+sqrt(4801))*exp((1/20)*sqrt(-1+sqrt(4801))*t)-(104999999/105000000)*t+_C1, w(t) = _C2+_C3*exp(-(1/20)*sqrt(-1+sqrt(4801))*t)+_C4*exp((1/20)*sqrt(-1+sqrt(4801))*t)+_C5*exp(-(1/20*I)*sqrt(1+sqrt(4801))*t)+_C6*exp((1/20)*sqrt(-1+sqrt(4801))*t)}</p>
<p>#SO THERE ARE 6 UNKOWN(C1...C6) SO I NEED 6 CONDITION. MY BOUNDRY CONDITIONS:</p>
<p>bs := u(0) = 0, (D(u))(0) = 0, w(0) = 0, (D(w))(0) = 0, w(teta) = 0, (D(w))(teta) = 0;</p>
<p>> r := dsolve({bs, sys1});<br>%;<br>Error, (in dsolve) invalid arguments; expected an equation, or a set or list of them, received: {{-17500000000*(diff(diff(diff(diff(w(t), t), t), t), t)) = 10500000000*(diff(u(t), t))-875000000*(diff(diff(diff(u(t), t), t), t))+10499999900, 210043750000*(diff(diff(u(t), t), t)) = -10500000000*(diff(w(t), t))+875000000*(diff(diff(diff(w(t), t), t), t))}}<br>></p>
<p>I tried to change the equations row. But ı dont understand where something wrong.I tried so many times. May u please find where ıt is wrong? </p>
<p> </p><p>b := 1;</p>
<p>h := 1;</p>
<p>A := b*h;</p>
<p>E := 210*10^9;</p>
<p>qr := 100;</p>
<p>Dp := (1/12)*E*b*h^3;</p>
<p>R := 20;</p>
<p>teta := 3;</p>
<p>sys1 := {(E.A+Dp/R^2)*(diff(u(t), `$`(t, 2))) = -E*A*(diff(w(t), t))/R+Dp*(diff(w(t), `$`(t, 3)))/R, -Dp*(diff(w(t), `$`(t, 4))) = E*A*(diff(u(t), t))/R-Dp*(diff(u(t), `$`(t, 3)))/R+E*A/R-100};</p>
<p>dsolve(sys1);</p>
<p>#THİS GAVE ME THE RESULTS LİKE THAT:</p>
<p>{u(t) = (1/4801)*_C3*(-1+sqrt(4801))^(3/2)*exp(-(1/20)*sqrt(-1+sqrt(4801))*t)-(1/4801)*_C4*(-1+sqrt(4801))^(3/2)*exp((1/20)*sqrt(-1+sqrt(4801))*t)-(1/4801*I)*_C5*(1+sqrt(4801))^(3/2)*exp(-(1/20*I)*sqrt(1+sqrt(4801))*t)-(1/4801)*_C6*(-1+sqrt(4801))^(3/2)*exp((1/20)*sqrt(-1+sqrt(4801))*t)+(1/4801)*_C3*sqrt(-1+sqrt(4801))*exp(-(1/20)*sqrt(-1+sqrt(4801))*t)-(1/4801)*_C4*sqrt(-1+sqrt(4801))*exp((1/20)*sqrt(-1+sqrt(4801))*t)+(1/4801*I)*_C5*sqrt(1+sqrt(4801))*exp(-(1/20*I)*sqrt(1+sqrt(4801))*t)-(1/4801)*_C6*sqrt(-1+sqrt(4801))*exp((1/20)*sqrt(-1+sqrt(4801))*t)-(104999999/105000000)*t+_C1, w(t) = _C2+_C3*exp(-(1/20)*sqrt(-1+sqrt(4801))*t)+_C4*exp((1/20)*sqrt(-1+sqrt(4801))*t)+_C5*exp(-(1/20*I)*sqrt(1+sqrt(4801))*t)+_C6*exp((1/20)*sqrt(-1+sqrt(4801))*t)}</p>
<p>#SO THERE ARE 6 UNKOWN(C1...C6) SO I NEED 6 CONDITION. MY BOUNDRY CONDITIONS:</p>
<p>bs := u(0) = 0, (D(u))(0) = 0, w(0) = 0, (D(w))(0) = 0, w(teta) = 0, (D(w))(teta) = 0;</p>
<p>> r := dsolve({bs, sys1});<br />%;<br />Error, (in dsolve) invalid arguments; expected an equation, or a set or list of them, received: {{-17500000000*(diff(diff(diff(diff(w(t), t), t), t), t)) = 10500000000*(diff(u(t), t))-875000000*(diff(diff(diff(u(t), t), t), t))+10499999900, 210043750000*(diff(diff(u(t), t), t)) = -10500000000*(diff(w(t), t))+875000000*(diff(diff(diff(w(t), t), t), t))}}<br />></p>
<p>I tried to change the equations row. But ı dont understand where something wrong.I tried so many times. May u please find where ıt is wrong? </p>
<p> </p>201152Sun, 16 Mar 2014 22:04:37 ZilkeilkeSolving simultaneous equations
http://www.mapleprimes.com/questions/201094-Solving-Simultaneous-Equations-?ref=Feed:MaplePrimes:Tagged With equations
<p>Could someone show me how to solve the following equations for real x, y and z.</p>
<p>Thanks</p>
<p>x^2 + 2yz^2 = 0,</p>
<p>y^2 - 3xz = 0, </p>
<p>1/3*x*y^2 + 2*y*z^3 = 0,</p>
<p>-1/3*y^4 - 6yz^4 = 0.</p>
<p> </p><p>Could someone show me how to solve the following equations for real x, y and z.</p>
<p>Thanks</p>
<p>x^2 + 2yz^2 = 0,</p>
<p>y^2 - 3xz = 0, </p>
<p>1/3*x*y^2 + 2*y*z^3 = 0,</p>
<p>-1/3*y^4 - 6yz^4 = 0.</p>
<p> </p>201094Sun, 09 Mar 2014 15:17:01 Zjohn125john125getting parametric equations
http://www.mapleprimes.com/questions/200992-Getting-Parametric-Equations?ref=Feed:MaplePrimes:Tagged With equations
<p>Hello Maple users friends,</p>
<p>I have two lines in the space (x,y,z) described by the equations in L1 and L2:</p>
<p> </p>
<p>L1:= {4*x + 3*y + z = 0, x + y - z - 15 = 0}:</p>
<p>L2:={12*x + 5*y + 7*z -13 = 0, 9*x + y -3*z - 5 = 0}:</p>
<p>I would like the get the parametric (with z=t) equations P1 and P2 of the two lines..</p>
<p>I see the "form" of such parametric equations P1 and P2 using "solve"</p>
<p>solve(L1, {x, y}); solve(L2, {x,y});</p>
<p> </p>
<p>but I do not know how to use those values to get my parametric equations P1 and P2 to continue with additional computation (area, volume etc).</p>
<p>Thanks for your attention and help.</p>
<p>JJ</p><p>Hello Maple users friends,</p>
<p>I have two lines in the space (x,y,z) described by the equations in L1 and L2:</p>
<p> </p>
<p>L1:= {4*x + 3*y + z = 0, x + y - z - 15 = 0}:</p>
<p>L2:={12*x + 5*y + 7*z -13 = 0, 9*x + y -3*z - 5 = 0}:</p>
<p>I would like the get the parametric (with z=t) equations P1 and P2 of the two lines..</p>
<p>I see the "form" of such parametric equations P1 and P2 using "solve"</p>
<p>solve(L1, {x, y}); solve(L2, {x,y});</p>
<p> </p>
<p>but I do not know how to use those values to get my parametric equations P1 and P2 to continue with additional computation (area, volume etc).</p>
<p>Thanks for your attention and help.</p>
<p>JJ</p>200992Sun, 23 Feb 2014 22:56:22 ZjeanjacquesvvidejeanjacquesvvideHow do I solve this system of PDEs in Maple?
http://www.mapleprimes.com/questions/200939-How-Do-I-Solve-This-System-Of-PDEs-In-Maple?ref=Feed:MaplePrimes:Tagged With equations
<p>Hi there,</p>
<p>I'm quite new to Maple so please forgive me! I have a system of partial differential equations I'm trying to solve in Maple as such below </p>
<p> </p>
<p>df/dt = f(1-f) - f * h</p>
<p>dg/dt = g(1-g) * Gradient(1-f * gradient(g))</p>
<p>dh/dt = (g - h) + Laplacian(h),</p>
<p>where f,g,h are functions of space and time (i.e. f(x,y,z,t)). I guess my first question is - is this possible in Maple to evaluate? (I'm currently unsure on ICs as I'm figuring it out from the model - it's a model for cancer growth I'm trying to evaluate but have a rough idea of what I'd use).</p>
<p>If it is possible, can you please share how I'd write this? Everytime I've tried I seem to be failing to define anything properly, so your expertise would be greatly appreciated!</p><p>Hi there,</p>
<p>I'm quite new to Maple so please forgive me! I have a system of partial differential equations I'm trying to solve in Maple as such below </p>
<p> </p>
<p>df/dt = f(1-f) - f * h</p>
<p>dg/dt = g(1-g) * Gradient(1-f * gradient(g))</p>
<p>dh/dt = (g - h) + Laplacian(h),</p>
<p>where f,g,h are functions of space and time (i.e. f(x,y,z,t)). I guess my first question is - is this possible in Maple to evaluate? (I'm currently unsure on ICs as I'm figuring it out from the model - it's a model for cancer growth I'm trying to evaluate but have a rough idea of what I'd use).</p>
<p>If it is possible, can you please share how I'd write this? Everytime I've tried I seem to be failing to define anything properly, so your expertise would be greatly appreciated!</p>200939Thu, 13 Feb 2014 12:11:40 ZocprodigyocprodigyEfficient method of repeatedly solving equations?
http://www.mapleprimes.com/questions/200907-Efficient-Method-Of-Repeatedly-Solving-Equations?ref=Feed:MaplePrimes:Tagged With equations
<p>Hi Maple Prime-ers!</p>
<p>I have a question about efficiency. I have a set of algebraic equations with some polynomials, that I would like to solve at different points. I've tried using a for-loop and a map-loop. Here is a example:</p>
<p> </p>
<blockquote>
<p>n:=10000; #Number of solving points<br>eq1:={b = ''a^2'', c = b^3/2, d = c^(1/2)*4 + b^2}; #Equation to solve</p>
<p>a := convert([seq(i,i=1..n)],Vector); #timesteps</p>
<p>ans := Vector[column](n)</p>
<p>## Try solving in a for-next loop<br>t1 := time():<br>for q from 1 to n do<br>ans(q):=solve(subs({'a' = a(q)},eq1)):<br>od:<br>t2 := time() - t1;</p>
<p>## try solving in a map loop<br>t1s := time():<br>ans_s := map(q->solve(subs({'a' = a(q)},eq1)),a);<br>t2s := time() - t1s;</p>
</blockquote>
<p>On my computer (2.2Ghz, 2 cores), these both take 115s to solve. Using Map over For-Next did not speed up computational speed. </p>
<p>The problem I wish to tackle has 12 equations, invovles 5th order polynomials, and n ~= 300000. Solving this set of equations takes 2-3 hours.</p>
<p>Anyone know a more efficient method? Thanks for reading :D</p>
<p> </p><p>Hi Maple Prime-ers!</p>
<p>I have a question about efficiency. I have a set of algebraic equations with some polynomials, that I would like to solve at different points. I've tried using a for-loop and a map-loop. Here is a example:</p>
<p> </p>
<blockquote>
<p>n:=10000; #Number of solving points<br />eq1:={b = ''a^2'', c = b^3/2, d = c^(1/2)*4 + b^2}; #Equation to solve</p>
<p>a := convert([seq(i,i=1..n)],Vector); #timesteps</p>
<p>ans := Vector[column](n)</p>
<p>## Try solving in a for-next loop<br />t1 := time():<br />for q from 1 to n do<br />ans(q):=solve(subs({'a' = a(q)},eq1)):<br />od:<br />t2 := time() - t1;</p>
<p>## try solving in a map loop<br />t1s := time():<br />ans_s := map(q->solve(subs({'a' = a(q)},eq1)),a);<br />t2s := time() - t1s;</p>
</blockquote>
<p>On my computer (2.2Ghz, 2 cores), these both take 115s to solve. Using Map over For-Next did not speed up computational speed. </p>
<p>The problem I wish to tackle has 12 equations, invovles 5th order polynomials, and n ~= 300000. Solving this set of equations takes 2-3 hours.</p>
<p>Anyone know a more efficient method? Thanks for reading :D</p>
<p> </p>200907Tue, 11 Feb 2014 23:24:59 Zteh_allchemistteh_allchemist6 equations , 6 unknowns?
http://www.mapleprimes.com/questions/200706-6-Equations--6-Unknowns?ref=Feed:MaplePrimes:Tagged With equations
<p>I am trying to solve a set of equations for a Fluid dynamics problem and I cannot get a result...Any ideas why?</p>
<p>rho := 1.184;<br>nu := 1.562*10^(-5);<br>ID := .15;<br>L := 24.5;<br>Kl := 12.69;<br>Ho := 50.52;<br>a := 2.1*10^(-5);<br>E := 0.1e-2; alpha := 1.05;</p>
<p>sys := {Re = ID*V/nu, hl = (f*L/ID+Kl)*V^2/(2*9.81), Vflow = (1/4)*Pi*ID^2*V, Hrequired = alpha*V^2/(2*9.81)+hl, Hrequired = -a*Vflow^2+Ho, 1/sqrt(f) = -1.8*log[10](6.9/Re+(E/(3.7))^1.11)};</p>
<p>solve(sys*{Re, V, f, hl, Vflow, Hrequired});<br>%;<br>Error, (in unknown) invalid input: Utilities:-SetEquations expects its 2nd argument, equations, to be of type set({boolean, algebraic, relation}), but received {{Re = (9603072983/1000000)*V, hl = (5096839959/100000000000)*((1633333333/10000000)*f+1269/100)*V^2, Vflow = (9/1600)*Pi*V, Hrequired = (5351681957/100000000000)*V^2+hl, Hrequired = -(21/1000000)*Vflow^2+1263/25, 1/f^(1/2) = -(9/5)*ln((69/10)/Re+27367561/250000000000)/ln(10)}}</p>
<p> </p><p>I am trying to solve a set of equations for a Fluid dynamics problem and I cannot get a result...Any ideas why?</p>
<p>rho := 1.184;<br />nu := 1.562*10^(-5);<br />ID := .15;<br />L := 24.5;<br />Kl := 12.69;<br />Ho := 50.52;<br />a := 2.1*10^(-5);<br />E := 0.1e-2; alpha := 1.05;</p>
<p>sys := {Re = ID*V/nu, hl = (f*L/ID+Kl)*V^2/(2*9.81), Vflow = (1/4)*Pi*ID^2*V, Hrequired = alpha*V^2/(2*9.81)+hl, Hrequired = -a*Vflow^2+Ho, 1/sqrt(f) = -1.8*log[10](6.9/Re+(E/(3.7))^1.11)};</p>
<p>solve(sys*{Re, V, f, hl, Vflow, Hrequired});<br />%;<br />Error, (in unknown) invalid input: Utilities:-SetEquations expects its 2nd argument, equations, to be of type set({boolean, algebraic, relation}), but received {{Re = (9603072983/1000000)*V, hl = (5096839959/100000000000)*((1633333333/10000000)*f+1269/100)*V^2, Vflow = (9/1600)*Pi*V, Hrequired = (5351681957/100000000000)*V^2+hl, Hrequired = -(21/1000000)*Vflow^2+1263/25, 1/f^(1/2) = -(9/5)*ln((69/10)/Re+27367561/250000000000)/ln(10)}}</p>
<p> </p>200706Mon, 06 Jan 2014 12:23:00 Zwhataboutcvewhataboutcve