use the Laplace transform to solve the given initial-value problem. y"+y'-2y=10e^{-t}, y(0)=0,y'(0)=1

CoormaBak9

CoormaBak9

Answered question

2020-12-17

use the Laplace transform to solve the given initial-value problem.y"+y2y=10et,y(0)=0,y(0)=1

Answer & Explanation

Latisha Oneil

Latisha Oneil

Skilled2020-12-18Added 100 answers

Step 1
Given y"+y2y=10et(1)
and y(0)=0,y(0)=1
Using the Laplace transform, (1)
S2y(s)Sy(0)y(0)+sy(s)y(0)2y(s)=10S+1
Step 2
(S2+S2)y(S).S.010=10s+1
(S2+S2)y(S)=1+10s+1
Y(s)=1S2+S2+10(S+1)(S2+S2)
=1(S+2)(S1)+10(S+1)(S1)(S+2)
=13(S+2)+13(S1)+53(S1)5S+1+103(S+2)
Y(s)=3S+2+2S15S+1
y(t)=e2t+etet for t>0

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?