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Hello all

I am trying to write  a tutorial about systems of linear equations, and I want to demonstrate the idea that when you have a system of 3 euqtions with 3 unknowns, the solution is the intersection point between these planes. Plotting 3 planes in Maple 2015 is fairly easy (you plot one and just drag the others in), but I don't know how to plot the intersection point. Can you help please ?

 

My equations are:

x-2y+z=0

2y-8z=8

-4x+5y+9z=-9

The intersection point is (29,16,3)

 

Thank you !

I want to solve these two differential equations. I have the initial conditions:
x(0)=0
y(0)=0
x'(0)=5.7
t'(0)=8.1
What am I doing wrong?

Hi

Anyone could help me in solving the following system of equations to get constants C1, C2, C3 and C4. MALPE give me this "soution may have been lost".  The MAPLE sheet is also attached.

 

restart:

Eq1:=simplify(C3*exp(-(1/4)*(C2*(x^2-2*0)+sqrt(C2*(x^2-2*0)^2+4*M*(x^2-2*0)*w1*(x^2-2*0)))/w1)+C4*exp((1/4)*(-C2*(x^2-2*0)+sqrt(C2*(x^2-2*0)^2+4*M*(x^2-2*0)*w1*(x^2-2*0)))/w1)-U) = 0;

C3*exp(-(1/4)*(C2*x^2+(x^4*(4*M*w1+C2))^(1/2))/w1)+C4*exp(-(1/4)*(C2*x^2-(x^4*(4*M*w1+C2))^(1/2))/w1)-U = 0

(1)

Eq2:=simplify(exp(-(1/4)*(C2+sqrt(C2^2+4*M*w1))*(x^2-2*0)/w1)*C3*x+exp((1/4)*(-C2+sqrt(C2^2+4*M*w1))*(x^2-2*0)/w1)*C4*x+C2-V-z) = 0;

exp(-(1/4)*(C2+(C2^2+4*M*w1)^(1/2))*x^2/w1)*C3*x+exp(-(1/4)*(C2-(C2^2+4*M*w1)^(1/2))*x^2/w1)*C4*x+C2-V-z = 0

(2)

Eq3:=simplify((-2*w2*w5*ln(C3*exp(-(1/2)*sqrt(w2*w4*(w2*w4+w3*w6))*C2*(x^2-2*0)/(w2*w4*w5))-C4)*sqrt(w2*w4*(w2*w4+w3*w6))+w2*w5*(-w2*w4+sqrt(w2*w4*(w2*w4+w3*w6)))*ln(exp(-(1/2)*sqrt(w2*w4*(w2*w4+w3*w6))*C2*(x^2-2*0)/(w2*w4*w5)))+C1*w3*w6*sqrt(w2*w4*(w2*w4+w3*w6)))/(sqrt(w2*w4*(w2*w4+w3*w6))*w3*w6)-1)= 0;

(-ln(exp(-(1/2)*(w2*w4*(w2*w4+w3*w6))^(1/2)*C2*x^2/(w2*w4*w5)))*w2^2*w4*w5+C1*w3*w6*(w2*w4*(w2*w4+w3*w6))^(1/2)-2*w2*w5*ln(C3*exp(-(1/2)*(w2*w4*(w2*w4+w3*w6))^(1/2)*C2*x^2/(w2*w4*w5))-C4)*(w2*w4*(w2*w4+w3*w6))^(1/2)+ln(exp(-(1/2)*(w2*w4*(w2*w4+w3*w6))^(1/2)*C2*x^2/(w2*w4*w5)))*(w2*w4*(w2*w4+w3*w6))^(1/2)*w2*w5-(w2*w4*(w2*w4+w3*w6))^(1/2)*w3*w6)/((w2*w4*(w2*w4+w3*w6))^(1/2)*w3*w6) = 0

(3)

Eq4:= simplify((-C2*x^2*w2*w4-.50*C2*x^2*w3*w6+sqrt(w2*w4*(w2*w4+w3*w6))*C2*x^2+2.*w2*w4*w5*ln(w3^4*w6^2*(C3^2*exp(-1.0*sqrt(w2*w4*(w2*w4+w3*w6))*C2*x^2/(w2*w4*w5))-2*C3*exp(-.5*sqrt(w2^2*w4^2+w2*w3*w4*w6)*C2*x^2/(w2*w4*w5))*C4+C4^2)/(w2*w4*(w2*w4+w3*w6)*C2^2))-5.544000000*w2*w4*w5-w3^2*w6)/(w3^2*w6)) = 0;

(-C2*x^2*w2*w4-.5000000000*C2*x^2*w3*w6+(w2*w4*(w2*w4+w3*w6))^(1/2)*C2*x^2+2.*w2*w4*w5*ln(w3^4*w6^2*(C3^2*exp(-(w2*w4*(w2*w4+w3*w6))^(1/2)*C2*x^2/(w2*w4*w5))-2.*C3*exp(-.5*(w2*w4*(w2*w4+w3*w6))^(1/2)*C2*x^2/(w2*w4*w5))*C4+C4^2)/(w2*w4*(w2*w4+w3*w6)*C2^2))-5.544000000*w2*w4*w5-w3^2*w6)/(w3^2*w6) = 0

(4)

solve({Eq1, Eq2, Eq3,Eq4}, {C1, C2, C3,C4});

Warning, solutions may have been lost

 

``

``

Download solution_lost.mw

 

 

hi guys, i have a complicated 4 set equations and i want to solve it,

one way is to find a solution for an equation and check it manually in other equations but i am looking for better method

eqq.mw

 

thanks

Hello everybody.

In the attached file, you find 6 equations. All of these parameters are known except "pd" and "qd". How can I find these two unknowns from 6 equations??? It should be pointed out that, "pd" and "qd" must contain "ud", "vd","wd" and "rd".

Thanks in advance.

D.mw

hi.I want to dsolve set of nonlinear equations with one unknown parameter ...is this possible with dsolve rule.in matlab this possible with bvp4c rule..please help me for this problem.if we should another rule please attached file reform.Thanks alot12.mw

I need to solve a set of equations but changing a constant each time.

For example, x+by=0, bx-y=10 where b=10,20.

I don't want to put it in a loop because, in loop, the equations are solved repeatedly. I want Maple to solve it only once and substitute b values automatically since I want to solve big set of equations faster.

Is there any option in Maple to do so with a single command

Hello,

From a simulation software, I obtain in a matlab file my differential equations in the following way :

C_p_e = C_state/C_c;
C_p_f = I_state/I_i;
R_p_e = R_r*C_p_f;
I_p_e = (Se_p_e-R_p_e)-C_p_e;

For theses expressions, I would like to do two operations :
1) Transform it into equations
2) Conduct substitutions so as to change the names of the variables with nicer names.

For this objectives, I could do with the following code:

restart;
eq1:=C_p_e = C_state/C_c;
eq2:=C_p_f = I_state/I_i;
eq3:=R_p_e = R_r*C_p_f;
eq4:=I_p_e = (Se_p_e-R_p_e)-C_p_e
allsubs:= proc(XX )
subs(C_p_e=fs(t),C_p_f=v(t),R_p_e=fd(t),I_p_e=fm(t),C_c=1/k,I_i=m,R_r=c,Se_p_e=fe(t),I_state=int(fm(t),t),C_state=int(v(t),t),XX)
end proc:
eq1_a:=allsubs(eq1);
eq2_a:=allsubs(eq2);
eq3_a:=allsubs(eq3);
eq4_a:=allsubs(eq4);

Now, I would like to automatisation the creation of the equations eq1, eq2, eq3, eq4. For the moment, to create these equations, I have done copy/ paste from matlab.

But, I would like to create these equations eq1, eq2, eq3, eq4 with a automative process from my matlab equations. The reason comes from the fact that I would like to make the same work on bigger system which are composed with numerous equations.

How can I create equations labeled eq1, ...eqn from a list of expressions from matlab ?

Thank you for your help

i am very new with Maple.

I have the following two equations:

x1=a-y1-d*y2;

x2=a-y2-d*y1;

I wish to express the first equation in terms of y1 and x2, so that

x1 = c - b*y1+d*x2;

where c=a-a*d and b=1-d^2. How can I get maple to rearrange the original equation x1 in term of y1, x2, c and b? 

 

hello

took this problem from a uk tv program.

4 dancers are initially at the 4 corners of a square, edge length 4 meters. every dancer moves towards the person on their left.

i want to know the equations of the spiral. the arc length of each path should be 4m.  also an animation of the 4 spirals would be great. 

dance.mw

under the heading "more spirals" the closest one is r(t)=1/t (decreasing modulus)

http://mathematische-basteleien.de/spiral.htm

 

       Calculation of RSCR mechanism as a  solution to underdetermined system of nonlinear equations.  

 

RSCR.mw 

https://vk.com/doc242471809_376439263
https://vk.com/doc242471809_408704758

RCCC mechanism
https://vk.com/doc242471809_375452868

Hi, I have 10 equation system and 10 unknown variables. I however, want to reduce the equations to 2 with two unknowns. I'm wondering how this could be done in maple. The variables are Y, q, yd, y*, yx, H,  pd, w, P and Pv. I intend to solve the equations for Y and w. 

Thanks in advance for your help. The maple file has also been attached.

 

Regards

Small_Open_Economy.mw

 

hi guys , i have this warning for solving a complicated equation with 7 parameters. how can i overcome to this warning ?

 


odesys := {(1/4)*(-4*r^(2+p+a)*p*a-11*r^(2+a+c)*a*c-4*r^(2+p+c)*p*c+22*r^(2+a+n)*a*n+8*r^(2+p+n)*p*n-22*r^(2+a+c)*a+8*r^(2+p+a)*p-8*r^(2+p+c)*p+22*r^(2+b)*b+32*r^(2+p)*p^2+32*r^(2+p)*p+22*r^(2+b)*b^2+22*r^(2+2*a)*a+65*r^(2+2*a)*a^2-8*r^(2+p+c)*p^2+8*r^(2+p+a)*p^2-22*r^(2+a+c)*a^2)/r^4+(1/4)*(4*r^(a+n)*n^2-2*r^(n+c)*n*c-4*r^(n+c)*n^2+3*r^(2*n)*n^2-4*r^(a+c)*c+8*r^(a+n)*n+4*r^(2*c)*c-8*r^(n+c)*n+4*r^m*m^2-4*r^d*d+8*r^m*m+4*r^m-4*r^d)/r^2}

{(1/4)*(-4*r^(2+p+a)*p*a-11*r^(2+a+c)*a*c-4*r^(2+p+c)*p*c+22*r^(2+a+n)*a*n+8*r^(2+p+n)*p*n-22*r^(2+a+c)*a+8*r^(2+p+a)*p-8*r^(2+p+c)*p+22*r^(2+b)*b+32*r^(2+p)*p^2+32*r^(2+p)*p+22*r^(2+b)*b^2+22*r^(2+2*a)*a+65*r^(2+2*a)*a^2-8*r^(2+p+c)*p^2+8*r^(2+p+a)*p^2-22*r^(2+a+c)*a^2)/r^4+(1/4)*(4*r^(a+n)*n^2-2*r^(n+c)*n*c-4*r^(n+c)*n^2+3*r^(2*n)*n^2-4*r^(a+c)*c+8*r^(a+n)*n+4*r^(2*c)*c-8*r^(n+c)*n+4*r^m*m^2-4*r^d*d+8*r^m*m+4*r^m-4*r^d)/r^2}

(1)

res := op(odesys);

(1/4)*(-4*r^(2+p+a)*p*a-11*r^(2+a+c)*a*c-4*r^(2+p+c)*p*c+22*r^(2+a+n)*a*n+8*r^(2+p+n)*p*n-22*r^(2+a+c)*a+8*r^(2+p+a)*p-8*r^(2+p+c)*p+22*r^(2+b)*b+32*r^(2+p)*p^2+32*r^(2+p)*p+22*r^(2+b)*b^2+22*r^(2+2*a)*a+65*r^(2+2*a)*a^2-8*r^(2+p+c)*p^2+8*r^(2+p+a)*p^2-22*r^(2+a+c)*a^2)/r^4+(1/4)*(4*r^(a+n)*n^2-2*r^(n+c)*n*c-4*r^(n+c)*n^2+3*r^(2*n)*n^2-4*r^(a+c)*c+8*r^(a+n)*n+4*r^(2*c)*c-8*r^(n+c)*n+4*r^m*m^2-4*r^d*d+8*r^m*m+4*r^m-4*r^d)/r^2

(2)

SOL1 := solve(identity(res = 0, r), {a, b, c, d, m, n, p})

Warning, solutions may have been lost

 

``


Download sol.mw

thanks

Hello,

This is the system of equations in term of sin and cos. I have used the command "solve" in Maple but it yielded only 2 solutions. I've tried to use with(RealDomain): It yielded more solutions but most of them were wrong.

 

 

f1 := -8100+(-30+70*cos(t1)-40*cos(t2))^2+(-70*sin(t1)+40*sin(t2))^2

f2 := (-20-80*cos(t3))^2+(-15+70*cos(t1)+10*cos(t1+t))^2+(-70*sin(t1)-10*sin(t1+t)+80*sin(t3))^2-5625

f3 := (-20-80*cos(t3))^2+(15+40*cos(t2)+10*cos(t1+t))^2+(-40*sin(t2)-10*sin(t1+t)+80*sin(t3))^2-5625

f4 := 10*cos(t1+t)*(30-70*cos(t1)+40*cos(t2))-10*sin(t1+t)*(70*sin(t1)-40*sin(t2))

 

Anybody know how to solve this system of equations to get the full set of roots?

Thank you very much in advance.

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