Cannot find nonhomogenous DE solution (should be easy?)

  • Thread starter gkirkland
  • Start date
  • #1
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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?

Capture_zpsc57ed194.jpg

Homework Statement





Homework Equations





The Attempt at a Solution

 

Answers and Replies

  • #2
ehild
Homework Helper
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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
 
  • #3
pasmith
Homework Helper
1,988
625

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?

Capture_zpsc57ed194.jpg

Try
[tex]
x_p = a\begin{pmatrix} 1 \\ -1 \end{pmatrix} te^{-t}
+ b\begin{pmatrix}1 \\ -5\end{pmatrix} e^{-t}
[/tex]
 

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