Given the differential equation:
$\dot{x} = y-x^2, \;\; \dot{y} = -x+y^2$
I have to find the solutions of this differential equation which move/lie on a line. I am not quite sure how to handle this problem, I started by writing $y = mx + q$, so:
$\dot{y} = m \dot{x} = m (y-x^2) = -x+y^2$
Solving this equation, I eventually arrived at $y = -x-1$. Now, a friend of mine told me this already is the solution, but I think it is only the line on which the solutions of the differential equation move. If so, how can I proceed in order to determine the solutions?
Thanks for any answers in advance.