Cannot find nonhomogenous DE solution (should be easy?)

[gkirkland]

Homework Statement

Determine the non-homogenous solution of the given differential equation.

Homework Equations

See 3.

The Attempt at a Solution

I have solved for the homogenous part, but as you can see in the link I am getting an unsolvable system of equations with the substitution method on the non-homogenous part. What am I doing wrong?

 

[ehild]

You have to choose an other trial function for xp, as the inhomogeneous part contains the same exponent as one of the exponents in the homogeneous part.

ehild

 

[pasmith]

Homework Statement

Determine the non-homogenous solution of the given differential equation.

Homework Equations

See 3.

The Attempt at a Solution

I have solved for the homogenous part, but as you can see in the link I am getting an unsolvable system of equations with the substitution method on the non-homogenous part. What am I doing wrong?

Try
$$x_p = a\begin{pmatrix} 1 \\ -1 \end{pmatrix} te^{-t} <br /> + b\begin{pmatrix}1 \\ -5\end{pmatrix} e^{-t}$$