Differential Equation - Linear Equations (Non - Homogeneous)

[cse63146]

Homework Statement

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

Homework Equations

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?

 

[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.

 

[cse63146]

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.

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