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

CoormaBak9 2020-12-17 Answered
use the Laplace transform to solve the given initial-value problem.y"+y2y=10et,y(0)=0,y(0)=1
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Expert Answer

Latisha Oneil
Answered 2020-12-18 Author has 100 answers
Step 1
Given y"+y2y=10et(1)
and y(0)=0,y(0)=1
By taking laplace transform of (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
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