I'm trying to solve an IVP with some difficulty. Actually, I'm having a problem just getting started. Problem:
$6y' - \frac{2}{y} = xy^4$
where
$y(0)=2, x>0$
To give you some context, I'm in a class which has thus far done Separable and Bernoulli ODEs to solve problems like this. I can't see how one can get either method to work. For example, my first thought was to divide by $y^4$ and treat it like a Bernoulli ODE. However, you can never rearrange the problem to have a simplification of something like $v$ and $v'$, as the $y^{-1}$ in the problem causes issues with this.
Any guidance on what is the way to move forward on this one?
Thanks!