how do i get the general solution of: dy/dx=(y/(sin(y)-x)) thanks
Last edited by mr fantastic; Nov 5th 2010 at 08:12 PM. Reason: Removed excessive !'s in title.
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Hmm. We have $\displaystyle \dfrac{dy}{dx}=\dfrac{y}{\sin(y)-x}$ $\displaystyle \dfrac{dx}{dy}=\dfrac{\sin(y)-x}{y}$ $\displaystyle \dfrac{dx}{dy}+\dfrac{x}{y}=\dfrac{\sin(y)}{y}.$ This is first-order linear in x(y).
so the IF is y? so you get y*(dx/dy)+x=ysiny from that you get: x=(1/y)*siny-cosy
Correct IF. However, the RHS is just sin(y), right? That should simplify things a bit for you.
ah yes i multiplied the if to the rhs! my bad! thanks very much!
You're welcome. Have a good one!