• Support PF! Buy your school textbooks, materials and every day products Here!

Differential Equations: Variation of Parameters

  • #1

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 [Broken]


I know i did something wrong because checking my answer by plugging Y(t) back in to the O.D.E , left hand side and right hand side dont 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
 
Last edited by a moderator:

Answers and Replies

  • #2
nevermind, i figured it out myself
 

Related Threads on Differential Equations: Variation of Parameters

Replies
1
Views
2K
Replies
1
Views
1K
Replies
2
Views
3K
Replies
2
Views
3K
Replies
1
Views
1K
Replies
1
Views
2K
Replies
1
Views
2K
Replies
2
Views
2K
Top