# Diff Eq- Nonhomogeneous Equations

## Homework Statement

Find a particular solution of the given equation.
$$y^''' + 4y^' = 3x-1$$

## Homework Equations

$$r^3 + 4r = 0$$
$$r = 0, r = 2i, r = -2i$$

## The Attempt at a Solution

$$y(x) = Ax-B$$
$$y^'(x) = A$$
$$y^''(x) = 0$$
$$y^'''(x) = 0$$

$$y(x)=(3/8)x^2 - (1/4)x$$

LCKurtz
Homework Helper
Gold Member
r=0 gives a constant as a solution of the homogeneous equation. So instead of trying Ax+B you must multiply by x and try ##y_p=Ax^2+Bx##.

LCKurtz
Homework Helper
Gold Member
Thanks! I have another question though,

$$4y^'' + 4y^' + y = 3xe^x$$

How do I start this?

The same way you started the other one. You find the complementary solution and then use Undetermined Coefficients for the particular solution. Surely your text discusses the method of Undetermined Coefficients, doesn't it?