# Math Help - Differential Equations General solution help.

1. ## Differential Equations General solution help.

how do i get the general solution of:
dy/dx=(y/(sin(y)-x))

thanks

2. Hmm. We have

$\dfrac{dy}{dx}=\dfrac{y}{\sin(y)-x}$

$\dfrac{dx}{dy}=\dfrac{\sin(y)-x}{y}$

$\dfrac{dx}{dy}+\dfrac{x}{y}=\dfrac{\sin(y)}{y}.$

This is first-order linear in x(y).

3. so the IF is y?

so you get y*(dx/dy)+x=ysiny
from that you get: x=(1/y)*siny-cosy

4. Correct IF. However, the RHS is just sin(y), right? That should simplify things a bit for you.

5. ah yes i multiplied the if to the rhs! my bad! thanks very much!

6. You're welcome. Have a good one!