# Homework Help: Solving Nonlinear System using Matlab

1. Jul 20, 2014

### xsw001

1. The problem statement, all variables and given/known data

Find the stable/unstable manifold for the nonlinear system dx/dt=y^2-(x+1)^2; dy/dt=-x

2. Relevant equations

3. The attempt at a solution

I'm trying to solve the below nonlinear system using Matlab, but got the following warning message. Any idea?

[x,y]=dsolve('Dx=y^2-(x+1)^2','Dy=-x')

Warning: Explicit solution could not be found.

I'm trying to find the stable/unstable manifolds. There are two critical pts for this nonlinear system (0,1) & (0,-1).

C.P.(0,1) is hyperbolic stable focus with complex eigenvalues => the eigenvectors are complex => there are No real manifolds.

C.P.(0,-1) is hyperbolic saddle point that has one positive eigenvalue, its eigenvector gives the direction of unstable manifold, there is another negative eigenvalue, its eigenvector gives the direction of stable manifold.

I'm trying to find the explicit solution for the nonlinear system so that I could find the stable/unstable manifolds.

Any suggestions would be appreciated!