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Question: Solving a Non-Linear Coupled System of ODEs

Question:Solving a Non-Linear Coupled System of ODEs

Jjjones98 45 Maple
ode syntax dsolve differential-equations
March 23 2019
1

I am working on a problem in geometry where I have ended up with a system of nonlinear ODEs in F and G where F and G are functions of a coordinate y, and A and B are both real constants.  I have included the worksheet where I am working on the equations.


Ric_Equations.mw
 

> 

dsolve((2*d^2*F(Y)*F(y)*G(y)/dy^2-(d*F(y)/dy*(d*G(y)/dy))*F(y)+(n-3)*(d*F(y)/dy)^2*G(y))/(4*F(y)*G(y)^2) = A, -(3*(2*d^2*F(y)/dy^2-(d*F(y)/dy)^2*G(y)-(d*F(y)/dy*(d*G(y)/dy))*F(y)))/(F(y)^2*G(y)) = B)

Error, (in dsolve) expecting an ODE or a set or list of ODEs. Received (1/4)*(2*d^2*F(Y)*F(y)*G(y)/dy^2-d^2*F(y)^2*G(y)/dy^2+(n-3)*d^2*F(y)^2*G(y)/dy^2)/(F(y)*G(y)^2) = A

  
> 

NULL

 

 I would like to solve these in as explicit a way as possible by obtaining expressions for F and G and was wondering how best to do this with Maple (it doesn't really matter if the explicit solutions are messy, as I just need to know that they exist and can be written down in some form).  I have tried using the dsolve command directly but I receive the error message which you can see above.

 

 

 

 

 
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