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Use the Laplace transform to solve the following initial value problem: y" – 3y = 0, y(0) = 2, y'(0) = −3 (1) First, using Y for the Laplace transform of y(t), i.e., Y = L(y(t)),

Use the Laplace transform to solve the following initial value problem: y" – 3y = 0, y(0) = 2, y'(0) = −3 (1) First, using Y for the Laplace transform of y(t), i.e., Y = L(y(t)),

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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y" – 3y' = 0, Use the Laplace transform to solve the following initial value problem: y(0) = 2, y′(0) = −3 (1) First, using Y for the Laplace transform of y(t), i.e., Y = L(y(t)), find the equation you get by taking the Laplace transform of the differential equation to obtain = 0 (2) Next solve for Y = = (3) Now write the above answer in its partial fraction form, Y Y (2s+3)/(s^(2)-3s) = 3/s (NOTE: the order that you enter your answers matter so you must order your terms so that the first corresponds to a and the second to b, where a < b. Also note, for example that −2 < 1) + -1/(S-3) A (sa) (4) Finally apply the inverse Laplace transform to find y(t) y(t) = 3-e^(3t) + B (s—b)
Transcribed Image Text:y" – 3y' = 0, Use the Laplace transform to solve the following initial value problem: y(0) = 2, y′(0) = −3 (1) First, using Y for the Laplace transform of y(t), i.e., Y = L(y(t)), find the equation you get by taking the Laplace transform of the differential equation to obtain = 0 (2) Next solve for Y = = (3) Now write the above answer in its partial fraction form, Y Y (2s+3)/(s^(2)-3s) = 3/s (NOTE: the order that you enter your answers matter so you must order your terms so that the first corresponds to a and the second to b, where a < b. Also note, for example that −2 < 1) + -1/(S-3) A (sa) (4) Finally apply the inverse Laplace transform to find y(t) y(t) = 3-e^(3t) + B (s—b)
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