Differential Equations: Variation of Parameters

[broodfusion]

Homework Statement

Find the particular solution to the differential equation using method of variation of parameters:

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

The Attempt at a Solution

Set 4y''-4y'+y=0

then the homogeneous solution is:

y= c1*e^(t/2)+c2*te(t/2)

set y1= e^(t/2), y2= te^(t/2)

then y1' = (1/2)*e^(t/2), y2' = (t/2+1)*e^(t/2)

Wronskian = W(y1,y2) = e^t

http://img140.imageshack.us/img140/1822/dif1.jpg


I know i did something wrong because checking my answer by plugging Y(t) back into the O.D.E , left hand side and right hand side don't check out.

By using method of undetermined coefficients, Y(t) = 2t^2*e^(t/2), which is the correct answer.

So question is what did i do wrong using method of variation of parameters?

Thanks

 

[broodfusion]

nevermind, i figured it out myself