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

1. Aug 3, 2010

### IKonquer

1. The problem statement, all variables and given/known data
Hi all, I'm trying to solve an ordinary differential equation. The problem is ty' + 2y = 4t^2

2. Relevant equations

3. 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.

1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

2. Aug 3, 2010

### qbert

Re: Ode

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