Hi! I am solving a problem, and I think I correctly arrived at $\ln\left|e^y-2x\ y\right|=C$. At any rate, I think I'll be left with $\ln\left|e^y-2x\ y\right|$, and I don't know how to solve for $y$!

Question

theeric · Answer

What I have done is this:

theeric · Answer

Put each side as the exponent of $e$. Then
$e^{\ln\left|e^y-2x\ y\right|}=e^C\\implies e^y-2x\ y=C$

where $C$ is still just an arbitrary constant.

anonymous · Answer

Let me guess, you solving a ODE? Not always it is posible to explicitly express y as function of x. Sometimes you just leave a general solution in implicit form

theeric · Answer

This is from an ODE.... I am supposed to solve it implicitly. Have I done that, then?

theeric · Answer

Assuming I got there correctly, I mean. I don't want to ask you to check my work.

anonymous · Answer

yes, you are done

theeric · Answer

Thank you! :)

anonymous · Answer

yw