how do i solve a set of coupled differential equations like these
for x(t) and y(t)
eqn1 := (D,2)(x)(t) = -a*sqrt(D(x)(t)^2+D(y)(t)^2)*D(x)(t),
eqn2 := (D,2)(y)(t) = g-a*sqrt(D(x)(t)^2+D(y)(t)^2)*D(y)(t)

i'm trying to solve a set of coupled differential equations and need help
eqn1 := (D,2)(x)(t) = -a*sqrt(D(x)(t)^2+D(y)(t)^2)*D(x)(t),
eqn2 := (D,2)(y)(t) = g-a*sqrt(D(x)(t)^2+D(y)(t)^2)*D(y)(t)

December 04 2006
Nasos 84
Hi,
Im using the display command to plot 3d surefaces/projections (which the also overlap on different occasions)on the same graph coming from different equations.
My question is how can i colour the surfaces with a command (its too hard to do it onthe graph)so i know to which equation each surface corresponds to? Is there an additional way offered from maple to distinuish the graphs from each other.
Finaly, I use the command labels=[x,y,z] to call my axis "Time of Fault Clearance,s" , "Magnitude of Fault Current" , "Parametr".How do i syntax a string?
Thanks for your time

Hi,
I am trying to solve these 6 equations with 6 unknowns. Unfortunately, "fsolve" does not give numerical results. Please let me know if there are other commands that I can use. I am using Maple 10.06 (Build ID 255401).
restart;
C := 2;
TY := .9;
Y := Vector(1 .. C, TY/C);
TM := 1;
DL := 5;
eq1 := X1 = (Y[1]+Z2)/TM;
eq2 := X2 = (Y[2]-Z2)/M2;
TX := X1+X2;
eq3 := M2 = (1-X1)*TM+X1/(1/TM+W1);
W0 := Y[1]/TM^2+Y[2]/M2^2;
EF := W0/(1-TX);
eq4 := W2 = EF+X1*min(W2, DL);
eq5 := W1 = (TX*EF-X2*W2)/X1;
eq6 := Z2 = Y[2]*max(0, W2-DL)/W2;
fsolve({eq2, eq5, eq1, eq3, eq6, eq4}, {M2, X1, X2, Z2, W1, W2});

Hi,
I've solved a system of nonlinear equations by hand, but I'm not sure if my answer is correct. I would like to verify my results with maple's output.
However, I am having some trouble using maple:
Here's my code:
> eq1:=2*(x*r) + 2*(y*s) + 2*(z*t)-(t^2) + (r^2)=0:
> eq2:=3*(x*(r^2)) + 3*(y*(s^2)) + 3*(z*(t^2))-(t^3)+(r^3) =0:
> eq3:=4*(x*(r^3)) + 4*(y*(s^3)) + 4*(z*(t^3))-(t^4)+(r^4)=0:
> fsolve({eq1, eq2, eq3});
Error, (in fsolve) number of equations, 3, does not match number of variables, 6
where r, s, and t are coefficients/constants and x, y, and z are variables.

Hello all,
I'm looking into visualizing/solving the Lotka-Volterra equations in Maple 10. In doing so I've run into a few problems:
1) When executing the following commands
```
> odeqs:= {diff(N(t),t) = a*N(t) - b*N(t)*P(t), diff(P(t),t)=c*N(t)*P(t) - d*P(t)}:
> # Growth rate of prey
> a:= 3;
> # Predatation rate
> b:= 2;
> # Growth of predators as a consequence of predation
> c:= 1;
> # Mortality rate of predators
> d:= 1/2;
> # Initial Conditions
> initConds:=[N(0)=(5/3),P(0)=(10/9)]];
>
> # Display number of prey as a function of time
> DEplot(odeqs, [N(t),P(t)], t=0..100, N=0..7, P=0..7, initConds,
```

November 24 2006
Nasos 84
Hi,
I would like to project the 3D surface generated from the following equation to the xy plane (2D):
Itouch50 := -0.4058074876e13*sqrt(1.+h)/(sqrt(ts)*(-500000000.0*ln((625.+125.*h+25.*h^2+5.*h^3)/h)*sqrt(1.+h)+587311661.7))
where x=Itouch50
y= ts
and z= h
Moreover, if possible, I would like to calculate the equation of the projection or the equations giving the upper and lower side of the projection.
Finally, if I had multiple equations as the initial one, would it be possible to create their accumulated projections on the same plane.
I know that Im asking for too much, but any help would be extremely appreciated.

p >Hello. I'm still kind of new to the practice of using a computer program to manipulate equations. I knew that one way to define an ellipse is as the locus of points P such that for 2 fixed points F1 and F2 the sum PF1 + PF2 is constant. I also know that in Cartesian coordinates, we get a formula of the form Ax2 + By2 = 1. If we set up our coordinate system such that F1 and F2 are on the x axis each a distance c from the origin and the maximum width of the ellipse is 2a, let's try to figure out A and B using MAPLE.

**> **

November 17 2006
hammer 4
Hi, I have a system of 3 coupled equations (3 unknowns) with complex numbers. I solved them with solvefor. I'm interested in the modulus (|a+ib|^2 = a^2 + b^2 ) and phase of each solution.
Because of that I used polar and abs (I have more interest in the modulus). In each case I ran simplify, despite of that the solutions are huge.
I would like to work with them in some spreadsheet (in order to set the parameters, evaluate the solutions, compare them with some experimental data and do some plotting).
Given that the solutions are huge I can just write them by hand where I want. In order to automatize that I've tried to use the VisualBasic command to cut&paste the formulas in VBA. The problem is that they are so long that the source code just gets broken.

I am taking a class where we have to solve second order differential equations (symbolically) for spherical and cylindrical coordinates. The equations are sometimes written
D(r^2*D(f(r)) (all are differented with respect to r, but it has r^2 between first and second differential.
Can Maple solve something in that form?

Hello everybody!
I again have a problem with "Dsolve numeric".
I solve a system of linear ODEs with boundary and continuity conditions.I got an error, which is associated with any internal procedure of Maple. For the sake of simplification, I reduced the order of equation from two fourth-order ODEs to the eight equations of the first order, but the same error is outputed.

Download 2847_problem-1-1.mwsView file details
Please help me clarify it.
Thank you

Hi everybody,
As a part of some general problem, I need to solve a system of non-linear ordinary differential equations.I try to get a numerical solution, so I use the "dsolve numeric" command. In same cases, the Maple print out two errors that I didn't find in his help instruction.
The first one is:
error, (in dsolve/numeric/bvp) cannot determine if this expression is true or false: 20*nerr

I have a large system of equations that takes a good hour to solve.
Each time I save and reopen the worksheet there is another lengthy recalculation on execution after which other operations are carried out.
I know how to save individual variables for reuse but what I would like to do is save the session so that the I can pick up from where I left off. Is this possible?

**UPDATE!!! ** I found that my blogpost appers in Maple reporter. You should know, that this blogpost was just a question about how to solve my problem better. Alec Mihailovs gave me and aswer and his solution of testing nested objects is much better. If you still want to use my piece of code, you should remove "set object" form "convertAMVStolist" procedure and replace all occurrences of "hastype" with "type" (as mentioned in comments below).

This piece of code should be able to test two objects (not of every type) for equivalence (like *testeq()* does). The benefit is, that it should be able to test also nested objects. Is there any other and more simple way how to do that? How to test nested objects in sets?