Question

Solve using separation of variables:

f''(x)g(y) + (1/x)f'(x)g(y) + (1/x^2)f(x)g''(y)=0

Answer 1

Divide by f(x)g(y)!

Answer 2

Hahahahahah... I'm embarrassed via the internet right now but okay thanks

Answer 3

don't try too hard... you might break a sweat :)

Answer 4

and multiply by x^2

Answer 5

try to get this
\[\large \frac{x^2 f''(x)+xf'(x)}{f(x)}=-\frac{g''(y)}{g(y)}=\lambda\]