Variation of parameters- 2nd order linear equation

[hahaha158]

Homework Statement

solve 4y''-4y'+y=16e^t/2

Homework Equations

v1= -∫ y₂g/w
v2= ∫ y₁g/w

The Attempt at a Solution

http://imgur.com/gxXlfdH

the correct answer is 2t^2 e^(t/2) instead of what i have though, i am not sure what i am doing wrong?

 

[pasmith]

Homework Statement

solve 4y''-4y'+y=16e^t/2

Homework Equations

v1= -∫ y₂g/w
v2= ∫ y₁g/w

The Attempt at a Solution

http://imgur.com/gxXlfdH

the correct answer is 2t^2 e^(t/2) instead of what i have though, i am not sure what i am doing wrong?

You need to divide by the coefficient of y'' before you start:
<br /> y&#039;&#039; - y&#039; + \frac14 y = 4e^{t/2} \equiv g(t).<br />