Solve the initial value problem below using the method of Laplace transforms.w"-4w'+4w=20t+64. w(-4)=-5 . w'(-4)=-4 .w(t)=?

tabita57i

tabita57i

Answered question

2021-09-14

Solve the initial value problem below using the method of Laplace transforms.
w"-4w+4w=20t+64

Answer & Explanation

Malena

Malena

Skilled2021-09-15Added 83 answers

Step 1
Given IVP:
w4w+4w=20t+64,w(4)=5,w(4)=4
Using Laplace transforms,
Lft{w4w+4w=20t+64right}
s2W(s)s(5)(4)4(sW(s)(5))+4W(s)=20s2+64s
s2W(s)+5s+44sW(s)20+4W(s)=20s2+64s
W(s)[s24s+4]=20s2+64s5s+16
Solving further,
Step 2
W(s)=20+64s5s2+16s2s2(s24s+4)
Now, taking inverse Laplace,
L1ft{W(s)right}=L1ft{20+64s5s2+16s2s2(s24s+4)right}
W(t)=L1ft{20+64s5s2+16s2s2(s2)(s2)right}
=L1ft{20+64ss2(s2)(s2)s2(165s)s2(s2)(s2)right}

Do you have a similar question?

Recalculate according to your conditions!

New Questions in Differential Equations

Ask your question.
Get an expert answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?