I'm asked to solve the initial value problem $$\dot{x}=f(x)\\x(0)=y$$ for $f(x)=(-x_1, -x_2+x_1^2, x_3+x_1^2)^T$. I think I need to put it in the form x(t)=Ax, but the $x_1^2$ terms are throwing me off..
I can't find a problem like this in the section nor the previous chapters.
Can someone point me in the right direction?
First solve $$ \dot x_1=-x_1 $$ Then insert the solution into $$ \dot x_2=-x_2+x_1^2\\ \dot x_3=x_3+x_1^2 $$ and solve both separately.