I'm trying to find a function $f(x,y)$ which applies the conditions $f_y(x,y)=x^2+2y$ and $f(x,x^2)=1$.
I tried to compute $f_x(x,x^2)=f_x(x,x^2)+2xf_y(x,x^2)$ so I get that $f_y(x,x^2)=0$. I don't really have a direction of how I should solve this. I'd love your help with this one.
Edit: Is there any solution without using integrals? I don't how to integrate with respect to one variable.
Thanks a lot!