Items tagged with equations

I am running Maple 11 with a mac-intel MacBook (13'' screen). I have been running a procedure for plotting a system of differentail equations that depend on an arbitrary parameter. The procedure works well for some "simple" parameters. For some more complicated parameters, the memory count (bottom right hand size) goes from near zero to over 500 M in six seconds ! A message appears: "kernel connection lost", and warns that such problems could be due to firewall settings, but all my firewall software is off. This procesure on these parameters works just fine with Maple 10 running in a PowerBook G4 (firewall connection also off).
A friend who has Mathematica suggested to me that Maple has no equivalent to the Mathematica Reduce command. Looking at the Reduce command on the Mathematica site, it says "Reduce[expr,vars] reduces the statement expr by solving equations or inequalities for vars and eliminating quantifiers." That sounds a lot like solve( ) to me so I attempted to use Maple's solve command on the following Mathematica Reduce( ) example. Reduce[x^2+y^2<><>
I am trying to enter equations from the following journal article: The link can be found in the Download 4865_Page from Lo_ApplMech_1962_V1_pp691-695.pdf
View file details Thus far I have been able to create equation (8) of the article in the attached worksheet: The link can be found in the View 4865_ring on MapleNet or Download 4865_ring
View file details
Dear Comrades, I'm trying to solve a system of coupled integral equations. Does anybody know how to use IntSolve? And what's the shared library? Do I have to download IntSolve from somewhere? And is this the best way to spolve integral equations if I did? Regards, Andrew
I have a system of equations where unkowns are functions of variables > eqns:= {a(s,y,z,t)+2*b(s,y,z,t)=0,3*a(s,y,z,t)-5*b(s,y,z,t)=0}; I would like to get the matrix associated to the system. I tested genmatrix but maple returns `equations are not linear ` Anyone have an idea of how to do this?
I am having this common problem when solving trig equations. I read "?solve" but missed something somewhere because I still don't know how to solve this problem. Taking a simple example of solve(sin(x)=1,x) the answer returned is Pi/2 and while Pi/2 is a correct answer, because of the periodic nature of the sin function there are others. So maple for some reason (which doesn't make sense to me at all)is limiting the range/domain and therefore not providing the complete answer which is Pi/2 +2nPi where n is any integer. I tried to force Maple to consider a larger range by using assume(0<>
Hi, First of all, I'm quite new to Maple and here, so I hope you will be patient with me..ehhehe. I've been struggling some days creating abstract vectorial equations with no luck. The equations have vectorial components as well as a matrix, it is the equation of motion, i.e: Inertia * dw/dt + w x Inertia.w = T Inertia is a matrix that I dont want to define now, and most of all I dont want to spread out its components, so it has to be all the time "Inertia". w is a angular speed vector and T is the Torque vector. Neither I want w to be defined or component separated (wx,wy,wz) at this point since I need to work with w for some change of coordinates .i.e w = w1 + ww1 . So I need to work in this abstract level.
Has Maple 11 changed the way you do mathematics? For me, it has. For me, Maple used to be a “mechanized mathematical assistant”. That is, when I was doing something mathematical, I would do it at my desk, with Maple on a computer beside me, to assist with some of the calculations. I used many sheets of paper; the papers were messy and disorganized. I would scribble equations, scratch out mistakes or recopy the good parts onto another sheet, have sub-results strewn about haphazardly, etc. With Maple 11, things are different. Now I do mathematics almost entirely within Maple. Now I keep everything in a document. I type formulae with 2D input, which looks much like how I would write things on paper, except neater. Graphics are interwoven with the formulae (and can be scribbled on). Mistakes are erased within the document. Sub-results are nicely put into collapsible subsections. The organization can, and of course does, change as I figure things out.
When I enter solve(x^4-x^3+1) I get 4 RootOf place holder solutions. For example RootOf(_Z^4-_Z^3+1, index = 1). This is very frustrating because I'm trying to obtain answers not place holders, and I cannot figure out how to make Maple solve the problem. Is Maple perhaps trying to tell me that it cannot solve the problem? If not, how do I force Maple to return answers instead of place holders, on this and similiar problems? Just as there is the quadratic equation for obtaining solutions to second degree equations, I understand that there are standard equations for solving cubics and quartics so I would be surprized if maple cannot solve x^4-x^3+1 symbolicly.
My class was given this question as a final homework but we can't figure out how to solve it. We have talked to the professor on multiple occasions but he will not provide any help. If anyone knows how to solve this using maple, please help. The question is below... solve x(t) = Ax(t)+B where B=[1 -1] A=[-1 0 1 2] and x(0) = (1 0) Sorry for the matrix formatting but, I don't know how to use the math equations here.
I have two equations with 3 variables(or perhaps n equations with n+1 variables) eq1:=0=c1*A1+c2*B1+c3*C1; eq2:=0=c4*A1+c5*B1+c6*C1; I can solve by e.g. solve({eq1,eq2},{A1,B1}) or any other combination of two of the variables. But if I follow the above by solve({eq1,eq2},{B1,C1}) I get then get an error. How do I find C1 as a function of A1? There must surely be a very way simple to do this. Did check the help pages but must have missed it if it is there.
There are two equations f'''+1/2*f*f''=0 and g'''+1/2*g*g''=0 boundary value f(0)=0 g(0)=0 f'(0)=g'(0)(is not zero) f''(0)=g''(0) f'(4)=1 g'(-4)=0.5 Because of two coupled boundary value (f'(0)=g'(0, f''(0)=g''(0)), it is difficult to solve. Could you tell me how to solve this equation using matlab? Thanks.
I am trying to create a plot for two differential equations but I'm not getting any graphs with the commands below. I'm not sure what's causing the problem and I've tried everything I can think of. Please help if you can. a := 2*ln(2) b := 1/5*ln(2) dose := proc (t) options operator, arrow; sum(2*Heaviside(t-6*n)-2*Heaviside(t-6*n-1/2), n = 0 .. 10) end proc J:=DEplot([diff(x(t), t) = dose(t)-a*x, diff(y(t), t) = a*x-b*y], [x, y], 0 .. 50, {[0, 0, 0]}, stepsize = .5, scene = ([t, x])) K:=DEplot([diff(x(t), t) = dose(t)-a*x, diff(y(t), t) = a*x-b*y], [x, y], 0 .. 50, {[0, 0, 0]}, stepsize = .5, scene = ([t, y]))
Hello, Given a system of differential equations as: C*V = O; where O is a null matrix and C is a 3X3 matrix as follows: Row 1: [rho*(alpha*I+omega*U*I), rho*U', alpha*I] Row 2: [0, rho*(alpha*I+omega*U*I), d/dy] Row 3: [alpha*I, d/dy, M^2*(alpha*I+omega*U*I)] The prime in Row 1 denotes differentiation with respect to y, and I is the unit imaginary number, d/dy is a differential operator. The vector V is given by: V = [u; v; w]; How do I use Maple to do a Gauss Elimination on the coefficient matrix which will give me separate equations for each of u, v and w. Or to be more specific, how do I represent the differential operator d/dy in a matrix

The attached Maple10 worksheet solves a system of differential equations. A plot of the solutions y1(t) (red curve) and y2(t) (green curve) appears below. Download 2353_fsolve-avoid.mws
View file details As a check, I want to use fsolve and the "avoid" option to find both times at which y1 has the same value as when y1=y2, but I'm having trouble. I would appreciate any advice on how I can get the "avoid" option to work for me. fsolve finds the earlier time easily enough (t=.9036852930e-1), but when I use the "avoid" option (highlighted statement below) to find the later time (t=.5225499740), I get the error "Error, (in fsolve) avoid = {.9036852930e-1} is an invalid option." The code is appended below. Thanks. Glenn ======== > restart; > with(plots): > sys:= Diff(y1(t),t)=-3*y1(t) + 2*y2(t), Diff(y2(t),t)=y1(t)-3*y2(t); > ic := y1(0)=1, y2(0)=5; d d sys := -- y1(t) = -3 y1(t) + 2 y2(t), -- y2(t) = y1(t) - 3 y2(t) dt dt ic := y1(0) = 1, y2(0) = 5 > odesol:=dsolve({sys,ic},{y1(t),y2(t)},type=numeric,output=listprocedure); odesol := [t = (proc(t) ... end proc), y1(t) = (proc(t) ... end proc), y2(t) = (proc(t) ... end proc)] > Y1:=eval(y1(t),odesol); Y2:=eval(y2(t),odesol); Y1 := proc(t) ... end proc Y2 := proc(t) ... end proc > Teq:=fsolve('Y1'(t)='Y2'(t),t); Teq := 0.5225499740 > Yeq:=Y1(Teq); Y2(Teq); Yeq := 1.45974175440983366 1.45974175447049736 > T1:=fsolve('Y1'(t)=Yeq); T2:=fsolve('Y2'(t)=Yeq); T1 := 0.09036852930 T2 := 0.5225499740 > fsolve('Y1'(t)=Yeq, t, avoid={T1}); fsolve('Y1'(t)=Yeq, t=T2); Error, (in fsolve) avoid = {.9036852930e-1} is an invalid option 0.5225499740 > Y1(%); 1.45974175440983366 > plot({Y1(t),Y2(t)},t=0..3);

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