What is the general solution for dy/dx=lnx/(xy+xy^3)?

[justinis123]

Homework Statement

Find the general solution of: dy/dx=lnx/(xy+xy^3)

Homework Equations

The Attempt at a Solution

In order to find the general solution, i rerrange the equation to:(y+y^3)dy=(lnx/x)dx,
then int(y+y^3)dy=int(lnx/x)dx, then i got 2(lnx)^2=2y^2+y^4. then i rerange y to the LHS and x to the RHS, but the answer looks strange.
Can anyone find where i did wrong?

 

[rock.freak667]

If you have t=ln(x), then dt=dx/x, so you are integrating dt/t, giving lnt.

So your final answer would not be (lnx)^2.