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**ODE, bernoulli equation --> leads to crazy integral !**

## Homework Statement

An Initial Value Problem, ODE (Bernoulli equation)

ODE: [x^2]*y' + 2*[x^3]*y = [y^2]*(1+2*[x^2])

IV: y(1) = 1/2

## Homework Equations

general form of Bernoulli's equation:

y' + a(x)y = b(x)*[y^n]

First order, linear ODE form:

y' + a(x)y = b(x)

## The Attempt at a Solution

I begin by simplifying the Bernoulli-type equation into a linear form, at which point I end up with an integral that I DO NOT KNOW HOW TO SOLVE.

I have either really messed up somewhere along the way to that Integral, or not and I just dont' know how to solve it.

Thanks for any help.