I need some help to solve a problem. I have the following system of SDE: system of SDE
I have to prove that $X_t^2 + Y_t^2 = (x^2 + y^2)e^t$
I have already shown with Ito lemma that $dZ_t=Z_tdt=(x^2+y^2)dt$ but I fail to integrate $dZ_t$ to have finally $Z_t=(x^2+y^2)e^t$.
Can you help me please? Many thanks for your time.