How to solve the ODE ty' + 2y = 4t^2

[IKonquer]

Homework Statement

Hi all, I'm trying to solve an ordinary differential equation. The problem is ty' + 2y = 4t^2

Homework Equations

The Attempt at a Solution

I got down to \int (t^{2})\frac{dy}{dt} + \int 2ty = \int 4t^{3}

I am not sure about how to integrate the left side of the equation. The dy/dt make y make the problem confusing.

 

[qbert]

just recognize
t^2 y' + 2 t y = (t^2 y)'
and use the fundamental theorem to say
\int f'(t) dt = f + C.