I have the equation$\begin{cases} x'(t)=x(t)+y(t) \\y'(t)= \mu y^2(t)+x(t)\end{cases}$ Cauchy problem $\begin{cases} x(0)= 1 + \mu \\y(0)=-2\end{cases}$ .
I must calculate $\frac{\partial x}{\partial \mu}\vert _{\mu=0}$.I tried a few hours, but I can't do that.
Help me . Please
In the attachments the calculus is not completed. The aim is only to show a method which will lead to the solution of the problem.This proves that it is theoretically possible to achieve it. But what remains to do would be a boring and arduous task.