The exact solution of nonlinear ordinary differential equations system

I want to find the exact solution of this nonlinear system:

y'(t)=-x(t)^2-2*x(t)+1;x'(t)=-y(t)^2-2*y(t)+1

but the dsolve function can not solve it and not return the exact

[Amith Kamath]

It would be much easier for someone to answer this if you could include details about what you tried, and also what error dsolve showed?

[ali ahmadi]

I insert

initiats='x(0)=1,y(0)=2';

dsolve('Dy=-x^2-2*x+1','Dx=-y^2-2*y+1',initiats)

and matlab could not get the result and stay on busy mood for a long time

Answer 1

[Walter Roberson]

Exact solution:

x(t) = y(t) = sqrt(2) - 1

There are alternative solutions, but they do not have any analytic form unless boundary conditions are known.

[ali ahmadi]

because I want to change the initial value I need to compute the exact by matlab. this is a constant!!!!

[Walter Roberson]

I am computing the solution for those boundary conditions; it may take a bit of time.

The general form of the solution is quite sensitive to the boundary conditions, and involves quite a number of integrations over the complex plane.