Solve the following initial value problem. (d2y/dt2)+25y=e2t, y(0)=0, y′(0)=0. (a) Find the Laplace transform of both sides of the equation to obtain the corresponding algebraic equation. Show the Laplace transform of y(t) by Y. (Not with Y(s).) Do not move any terms from one side of the equation to the other until you get to part (b) of the question. ...?....=...?... (b) Solve the Y transform from the equation you obtained and find its simple fractions. (Calculate the unknown coefficients to be written to the numerators.) (image) (c) Obtain the solution y(t) by calculating the inverse Laplace transform of the transform you found. y(t)= ?
Solve the following initial value problem. (d2y/dt2)+25y=e2t, y(0)=0, y′(0)=0. (a) Find the Laplace transform of both sides of the equation to obtain the corresponding algebraic equation. Show the Laplace transform of y(t) by Y. (Not with Y(s).) Do not move any terms from one side of the equation to the other until you get to part (b) of the question. ...?....=...?... (b) Solve the Y transform from the equation you obtained and find its simple fractions. (Calculate the unknown coefficients to be written to the numerators.) (image) (c) Obtain the solution y(t) by calculating the inverse Laplace transform of the transform you found. y(t)= ?
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Solve the following initial value problem.
(d2y/dt2)+25y=e2t, y(0)=0, y′(0)=0.
(a) Find the Laplace transform of both sides of the equation to obtain the corresponding algebraic equation. Show the Laplace transform of y(t) by Y. (Not with Y(s).) Do not move any terms from one side of the equation to the other until you get to part (b) of the question.
...?....=...?...
(b) Solve the Y transform from the equation you obtained and find its simple fractions. (Calculate the unknown coefficients to be written to the numerators.)
(image)
(c) Obtain the solution y(t) by calculating the inverse Laplace transform of the transform you found.
y(t)= ?
Transcribed Image Text:1
Y =
s+
s – 2
s2 + 25
||
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