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Solve the initial value problem below using the method of Laplace transforms. y" - 2y' - 8y = 0, y (0) = 4, y´ (0) = 22 y(t) = (please an answer in terms of e.)

Solve the initial value problem below using the method of Laplace transforms. y" - 2y' - 8y = 0, y (0) = 4, y´ (0) = 22 y(t) = (please an answer in terms of e.)

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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Solve the initial value problem below using the method of Laplace transforms. y" - 2y² - 8y = 0, y (0)= 4, y´(0) = 22 y(t) = (please an answer in terms of e.) Table of Laplace Transforms F(s) = L{f(t)} 1 f(t) 1 t eat t", n=1,2,... sin kt cos kt S S 1 1 2 S S>0 1 s-a n! n+1 S>0 " k 2 s²+k² S 2 s+k 2 S>0 S>0 " 2' S>0 S>0 Properties of Laplace Transforms L{f+g} = L{f}+ L{g} L{cf} = c£{f} for any constant c L{f'} (s) = s£{f}(s)-f(0) Lf''(s) = s²L{f}(s)-sf(0) - f'(0) L {f(n)} (s) = s^£{f}(s) -sn-¹f(0)-sn-²₁'(0)--(n-1)(0) £¯¹ {F₁+F₂} = £¯¹ {F₁} + £¯¹ {F2} L-¹{cF} = CL-¹ {F}
Transcribed Image Text:Solve the initial value problem below using the method of Laplace transforms. y" - 2y² - 8y = 0, y (0)= 4, y´(0) = 22 y(t) = (please an answer in terms of e.) Table of Laplace Transforms F(s) = L{f(t)} 1 f(t) 1 t eat t", n=1,2,... sin kt cos kt S S 1 1 2 S S>0 1 s-a n! n+1 S>0 " k 2 s²+k² S 2 s+k 2 S>0 S>0 " 2' S>0 S>0 Properties of Laplace Transforms L{f+g} = L{f}+ L{g} L{cf} = c£{f} for any constant c L{f'} (s) = s£{f}(s)-f(0) Lf''(s) = s²L{f}(s)-sf(0) - f'(0) L {f(n)} (s) = s^£{f}(s) -sn-¹f(0)-sn-²₁'(0)--(n-1)(0) £¯¹ {F₁+F₂} = £¯¹ {F₁} + £¯¹ {F2} L-¹{cF} = CL-¹ {F}
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