Trying to find laplace transform x(s) that satisfies x′(t)=x(t)−t?

Nayeli Osborne 2022-10-14 Answered
Trying to find laplace transform x(s) that satisfies x ( t ) = x ( t ) t?
Taking the Laplace transform of the equation
x ( t ) = x ( t ) t ,
we get
s x ( s ) x ( 0 ) = x ( s ) 1 s 2 ,
right? So if x ( 0 ) = 1, don't you get
x ( s ) = 1 1 s 2 s 1 ?
When I take the inverse laplace of this I get 2pi*i, how do I know this works?
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Answers (1)

Marlene Welch
Answered 2022-10-15 Author has 23 answers
1 1 s 2 s 1 = s 2 1 s 2 ( s 1 ) = s + 1 s 2 = 1 s + 1 s 2 .
How did you get zero for the inverse Laplace transform?
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