I know how to handle seperable first order ODEs, nth roots, and initial value problems. But I'm a touch confused about what to do when they all appear in the same problem.

For this:

$\displaystyle xy^3y' - 2x = 3$

where:

$\displaystyle x > 0$

$\displaystyle y(1) = -1$

We can get the general solution of

$\displaystyle y = (12ln(x) + 8x + C)^{\frac{1}{4}}$

But I'm a bit confused at to whether I should be getting the four roots of $\displaystyle y$ with $\displaystyle C$ first, or if I should be trying to solve for $\displaystyle C$ using the initial value given first, etc...

How is this best handled?