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Laplace transform

  • Thread starter Ry122
  • Start date
  • #1
565
2
I need to find the laplace transform of
y''(t)-y(t)=0 with initial conditions y(0)=1 and y'(0)=3

My attempt:
Ly''(t)=(s^2)F(s)-s(1)-(3)
Ly'(t)=sF(s)-1
so (s^2)F(s)-s(1)-(3)-sF(s)-1=0
I need to isolate F(s) so
F(s)=-(2/s^2)
Is this correct?
 

Answers and Replies

  • #2
Cyosis
Homework Helper
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You're solving for a different differential equation than the one you have listed. You are solving [itex]y''(t)-y'(t)=0[/itex]. That said you still made some mistakes. Your first two steps are correct, but then when you subtract the two you make a minus sign error. It should be,

[tex]s^2 F(s)-s-3-(s F(s)-1)=s^2 F(s)-s-3-sF(s) \textcolor{red}{+} 1=0[/tex].

I am not sure how you isolated the F(s), something seems to have gone wrong there as well. You can write it like,

[tex](s^2-s)F(s)-(s+2)=0[/tex]
 
  • #3
HallsofIvy
Science Advisor
Homework Helper
41,792
920
You wrote the problem as y"- y= 0, but you solved y"- y'= 0.
 

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