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I used implitplot to plot solutions to some (tricky) equations in 2 variables, of the form implicitplot([f(x,y)=0]).  Now I have a (tricky) change of parameterization G:R^2->R^2 of the form G(x,y)=(g(x,y),h(x,y)). I'd like to plot the image of the solution set of f(x,y)=0 under the map G. Of course, if I could invert G I'd implicitplot           G^(-1)(f(x,y))=0, but the functions I have dont lend themselves to this.

 

Presumably MAPLE stores the points it plots somewhere, and I should be able to apply G to this set of points. But I don't know how to approach this. Anybody know? 

eq1:=
(1/4)*D^2*Pi-(1/4)*D^2*arccos((-D+2*h)/D)-(1/2)*sqrt(h)*sqrt(D-h)*D+h^(3/2)*sqrt
(D-h);
                          
eq2 :=
-(1/2)*sqrt(h)*sqrt(D-h)*D+h^(3/2)*sqrt(D-h)+(1/4)*D^2*arcsin((-D+2*h)/D)+(1/8)*
D^2*Pi;

These equations are the same. yet simplify(eq1-eq2,trig);
<>0
The Mathematica COMMAND FullSimplify[..] gets zero.

Hi everyone,

I am a new user of maple and i want to know the procedures to follow when solving 4 differential equations simultaneously.

e.g

ds/dt=Λ0-βcSI/N-μS

dL/dt=Λ1+βcSI/N-μ1L+ΑcIT/N

dI/dt=kL-μ2I

dT/dt=r1L+r2I-ΑcIT/N-μT

Any help will be highly appreciated. Regards

Suppose I have a set of P polynomial equations in terms of N variables which are the coefficients of the equations. The equations are generated by the main program and are not known beforehand.

Example (P = 2):

e1 := c1 + 2*c2 + (c3+3*c4)*x*y + (c5+c6)*y^2 +(c8-2)*y^3*x^2 = 0;
e2 := (c4 + 2*c5 + c7)*x + (c9+ 2*c3+5*c4)*x^2 + (2*c7+5*c5+c6)*y^2*x^3 =0;

Because e1 and e2 must be zero for all x and y this implies that all the coefficients must be zero:

c1 + 2*c2 = 0
c3+3*c4 = 0 etc

This gives M linear equations in terms of N unknowns with N > M.

Given the P equations is there a way to automatically set up the M equations and solve for the N unknowns? In some cases it is possible that there are specific values of some of the c's eg c8 = 2 otherwise some of the c's will be expressed in terms of the other c's eg c1 = - 2*c2.

Thanks.

Suppose one sets a system of differental equations in vector form, say 2 ODE's, like this:

restart;
with(LinearAlgebra):
ode:=Vector([diff(x(t),t),diff(y(t),t)])=Vector([2*x(t)+y(t),3*y(t)-x(t)]);

Then to solve these, what would be an easy way to do it, without having to rewrite them again manually as a set, as what one would normally do. Clearly one needs to map dsolve, and also convert the vectors to a set somewhere? I am not able to get the syntax right.

Is there an easy way to automatically convert/rewrite the above to

ode2:= diff(x(t),t)=2*x(t)+y(t)  ,   diff(y(t),t)=3*y(t)-x(t);

so that I can just do

dsolve({ode2},{x(t),y(t)});

Or, a way to map dsolve directly into the first from as shown?( the Vector = Vector form).

Himmelblau.mw

     On the basis of Dragнilev method…

     Is there anyone interested in the algorithm to reduce the distance between the points of the given constraints? The algorithm is adapted for use in R ^ n. This is an example of its work on the surface:  
f = - (x1 ^ 2 x2-.3) ^ 2 - (x1 x2 ^ 2-.7) ^ 2 - 5;  

     Approximate description of the algorithm in pictures.

Aslam-u-Alikum...How are you? Hope you will be fine. I want nontriavial solution of the System of equations urgently please help me .Help.mw

Aslam-u-Alikum... How are you. Hope you will be fine. I want to solve nonlinear Equation for the root 0, 4.4934, 7.7253,10.9041,14.0662,17.2208, but my code give the solutions in Rootof form. Please help me as early as possible...Help.mw

Aslam-ul-Alikum I need some help urgently. I want to compare the coefficients of like powers of Y_1*Y_2, please help how i compare it in mapleHelp.mw

Aslam-ul-Alikum I need some help urgently. I want to compare the coefficients of like powers of Y_1*Y_2, please help how i compare it in maple

In a "If" conditional statement, maple returns

Error, cannot determine if this expression is true or false: 1.551691464 < (5/6)*Pi

I want to find the parameters m to the  equation x^4 -(3*m+2)*x^2 + 3*m+3 = 0 has four distinct solutions and all of them were less than 2. I tried

eq:= x^4 -(3*m+2)*x^2 + 3*m+3:

sol:=[solve(eq=0,x)]:

d:=discrim(eq,x):

solve([d>0,sol[1]<2,sol[2]<2,sol[3]<2,sol[4]<2],m):

allvalues(%);

How to reduce my code?

I am not sure if this is a general problem.  And I am considering the best way to evaluate the expression (Equation) when it contains variables which have been modified by using assume.   Here is a tiny test example:

restart;
assume(a>0,x>0);
int(int(x^2/y^2,y=1/x..x),x=1..a);S:=%:  
                        1  4   1   1  2

Dear All:

  I met an strange problem when using fsolve() function in maple. the following is my system equations, ILr0,Vcr0,M,T1 is the values i need to solved by maple . 

   ILr2+ILr0=0,Vcr0+Vcr2=0,ILr1=ILm1,Iout*RL=Vout   (1)  where

 

   ILr2--> ILr0*f1(T1)+Vcr0*f2(T1)+M*f3(T1);

   Vcr2--> ILr0*g1(T1)+Vcr0*g2(T1)+M*g3(T1);

   ILr1,ILm1-->  ILr0*h1(T1)+Vcr0*h2(T1)+M*h3(T1);

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