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y" + 2y'- 3y = 2t² - 10cos(2t) + 3sin(4t) -e³t where y(0) = 2 and y'(0) = -4

y" + 2y'- 3y = 2t² - 10cos(2t) + 3sin(4t) -e³t where y(0) = 2 and y'(0) = -4

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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pls give me the complete solution to this. 2nd pic is the answer.

1. Solve the following differential equation using Laplace method with respect to the given initial conditions: y" + 2y' - 3y = 2t² - 10cos(2t) + 3sin (4t) -e³t where y(0) = 2 and y'(0) = -4
Transcribed Image Text:1. Solve the following differential equation using Laplace method with respect to the given initial conditions: y" + 2y' - 3y = 2t² - 10cos(2t) + 3sin (4t) -e³t where y(0) = 2 and y'(0) = -4
1. Input interpretation: solve Result: y(t) = == 8 13 y" (t) + 2 y' (t)-3 y(t) = 2t² - 10 cos(2 t) + 3 sin(4 t) - e³t 3t y(0) = 2 y'(0) = -4 2t² 3 sin(2 t) 8t + 57 425 -3t 56051 e 70 200 sin(4 t) + + 14 13 177 et 136 cos(2 t) 3t 12 24 425 cos(4 t) - 28 27
Transcribed Image Text:1. Input interpretation: solve Result: y(t) = == 8 13 y" (t) + 2 y' (t)-3 y(t) = 2t² - 10 cos(2 t) + 3 sin(4 t) - e³t 3t y(0) = 2 y'(0) = -4 2t² 3 sin(2 t) 8t + 57 425 -3t 56051 e 70 200 sin(4 t) + + 14 13 177 et 136 cos(2 t) 3t 12 24 425 cos(4 t) - 28 27
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