Question

How to solve for f(x)?

Answer 1

\[\Huge y f '(xy)=f'(x)\]

Answer 2

Integrating and using by parts on LHS is kinda tricky

Answer 3

\[\LARGE \cancel y f(xy) \times \frac{1}{ \cancel y}-\int\limits \frac{y'}{y} f(xy) dx=f(x)\]

Answer 4

if im right..now its alot messy