# Differential Equation - Linear Equations (Non - Homogeneous)

1. Mar 25, 2009

### cse63146

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

Find the general solution of $$\frac{dy}{dt} + 2y = 3t^2 + 2t -1$$

2. Relevant equations

3. The attempt at a solution

So just worrying about the right side

$$y_p = at^2 + bt + c$$

so $$\frac{dy_p}{dt} + y_p = 2at + b +at^2 + bt + c = 3t^2+2t - 1$$

$$at^2 = 3t^2 \rightarrow a =3$$
$$2(3)t + bt = 2t \rightarrow b = -4$$
$$(-4) + c = -1 \rightarrow c = 3$$

Is that part right?

2. Mar 25, 2009

### Dr.D

Is that part right?

Substitute it back in and see if it is right? Far better that you learn to check it yourself than for you to ask someone else if it is right.

3. Mar 25, 2009

### cse63146

God, why didn't I think of that? Thank you.