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Find the Laplace transform Y(s) of the solution y(t) of the initial value problem where y"-2y+2y=f(t), f(t)= y(0)=2, y'(0)=3 12 for 0

Find the Laplace transform Y(s) of the solution y(t) of the initial value problem where y"-2y+2y=f(t), f(t)= y(0)=2, y'(0)=3 12 for 0

Advanced Engineering Mathematics
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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Find the Laplace transform Y(s) of the solution y(t) of the initial value problem where y"-2y+2y=f(t), y(0)=2, y'(0)=3 12 sin(t-л) You do not have to take the inverse Laplace transform to solve for y(t). f(t)= for 0≤t<n for t≥n.
Transcribed Image Text:Find the Laplace transform Y(s) of the solution y(t) of the initial value problem where y"-2y+2y=f(t), y(0)=2, y'(0)=3 12 sin(t-л) You do not have to take the inverse Laplace transform to solve for y(t). f(t)= for 0≤t<n for t≥n.
j(t)=L¹ {J(s)} 1 t", n = positive integer ear et", n = positive integer sin (bt) cos(bt) ear "sin (bt) ear 'cos (bt) Elementary Laplace's transforms eat j(t) sinh(at) u(t-c)= cosh(at) 1, t≥ c 0, t<c u(t-c) j(t-c) j(n) (t) J(s) = L{j(t)} 113 S 1 s-a n! S²+1 n! - a)"+1 s-a s>0 b s² + b² S 5² + b²² \n+1" s> a b (s-a)² + b² е s>0 s-a (s-a)² + b² -Cs S s> a s>0 J(s-a) s>0 a 3²0²² s>lal S s²-a² s> a S 3²-g² s>lal S s> a s>0 e-cs J(s) s"J(s) — s"−¹ j(0) — s"−² j'(0) — ...—– j(¹−¹) (0)
Transcribed Image Text:j(t)=L¹ {J(s)} 1 t", n = positive integer ear et", n = positive integer sin (bt) cos(bt) ear "sin (bt) ear 'cos (bt) Elementary Laplace's transforms eat j(t) sinh(at) u(t-c)= cosh(at) 1, t≥ c 0, t<c u(t-c) j(t-c) j(n) (t) J(s) = L{j(t)} 113 S 1 s-a n! S²+1 n! - a)"+1 s-a s>0 b s² + b² S 5² + b²² \n+1" s> a b (s-a)² + b² е s>0 s-a (s-a)² + b² -Cs S s> a s>0 J(s-a) s>0 a 3²0²² s>lal S s²-a² s> a S 3²-g² s>lal S s> a s>0 e-cs J(s) s"J(s) — s"−¹ j(0) — s"−² j'(0) — ...—– j(¹−¹) (0)
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