Undergrad Differential equation with two terms

[kent davidge]

I'm trying to solve a differential equation of the form $$\frac{A'(x)}{A(x)}f(x,y) = \frac{B'(y)}{B(y)}$$ where prime denotes differentiation. I know that for the case $f(x,y) = \text{constant}$ we just equal each side to a same constant. Can I do that also for the case where $f(x,y)$ is not constant? (I know $f(x,y)$ explicitely, if that helps.)

Edit: I'm trying to find both $A(x)$ and $B(y)$.

 

[kent davidge]

Oh, never mind. It's just a matter of breaking up $f(x,y)$ into parts. Sometimes writing down an equation in a more abstract form like I did here helps in getting the cake. :)