Nonhomogeneous linear differential equation

[HACR]

Homework Statement

solve for y(x).

[tex]y"'-6y"+11y'-6=e^{4x} [/tex]

Homework Equations

Wronskian determinant. Method of variations.

The Attempt at a Solution

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

 

[HACR]

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