# Nonhomogeneous linear differential equation

1. Jan 15, 2012

### HACR

1. The problem statement, all variables and given/known data
solve for y(x).

$$y"'-6y"+11y'-6=e^{4x}$$

2. Relevant equations

Wronskian determinant. Method of variations.

3. The attempt at a solution

Supposing that [u', v', w'] are the solutions, wronskian det=W is $$10e^{6x}$$
By use of $$x_k=\frac{det(M_{k})}{det(x)}$$, I got $$u'=\frac{1}{4}e^{8x},v'=\frac{-1}{9}e^{9x}, w'=\frac{-1}{7}e^{7x}$$. Integration gives $$y=\frac{1}{10}e^{2x}-\frac{1}{30}e^{3x}-\frac{e^{x}}{10}$$.

Last edited: Jan 15, 2012
2. Jan 16, 2012

### HACR

The answer has four whereas i came up with only 3 since the roots are 1,2, and 3 respectively. I think $$W=2e^{6x}$$