Question

Can someone help me set up this diff eq? I will write it in math below. I tried to use t=uy and dt=udy+y but really didn't get anything workable.

Answer 1

\[3(1+t^2)\frac{ dy }{ dt }=2ty(y^3-1)\]

Answer 2

I would re-arrange it as
\[ \frac{3}{y(y^3-1)} dy=\frac{2t}{t^2+1} dt \]
the right hand side is of the form du/u with u= (t^2+1)
the left side can be separated using partial fractions
(see http://www.purplemath.com/modules/partfrac.htm)