Solve Ay′′+By′+Cy=f(t) by Laplace Transform

4enevi 2022-10-29 Answered
Solve Ay′′+By′+Cy=f(t) by Laplace Transform
Here, y 0 = y 0 = 0 and f ( t ) = n for t 0 < t < t 0 + 1 n
Taking the Laplace transform of both sides, I've found that
L ( y ) = L ( f ) A s 2 + B s + C
and
L ( f ) = 0 f ( t ) e s t d t = n ( e s t e s ( 1 / n + t ) ) s
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Answers (1)

Zackary Mack
Answered 2022-10-30 Author has 12 answers
Note that we have the limit
lim n n ( e s t e s ( 1 / n + t ) ) s = e s t s lim n n ( 1 e s / n ) = e s t s × s   = e s t
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