For $f: \mathbb{R} \to \mathbb{R}$ differentiable, and inverse function which monotonically increasing. I'd love your help with finding $y$ from the following f'(y)y'=xf(y).
This is what I did so far:
\frac{f'(y)y'}{f(y)}=x\Rightarrow \frac{f'(y)\frac{dy}{dx}}{f(y)}=x\Rightarrow \int \frac{d(f(y))}{f(y)}=\int\frac{ f'(y)dy}{f(y)}=\int x dx\Rightarrow \ln f(y)=\frac{x^2}{2}.
What should I do from here?
Thanks a lot!