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Use the Laplace transform to solve the following initial value problem: y" - y' - 20y= 0, (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 (2) Next solve for Y = y(0) 9, y(0) 9 0 A (3) Now write the above answer in its partial fraction form, Y + a B 8-b (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

Use the Laplace transform to solve the following initial value problem: y" - y' - 20y= 0, (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 (2) Next solve for Y = y(0) 9, y(0) 9 0 A (3) Now write the above answer in its partial fraction form, Y + a B 8-b (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

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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Use the Laplace transform to solve the following initial value problem: " - y' - 20y= 0, (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 (2) Next solve for Y = A (3) Now write the above answer in its partial fraction form, Y + a B 8-b = y(0) 9, y'(0) = 9 0 (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) Y = (4) Finally apply the inverse Laplace transform to find y(t) y(t) =
Transcribed Image Text:Use the Laplace transform to solve the following initial value problem: " - y' - 20y= 0, (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 (2) Next solve for Y = A (3) Now write the above answer in its partial fraction form, Y + a B 8-b = y(0) 9, y'(0) = 9 0 (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) Y = (4) Finally apply the inverse Laplace transform to find y(t) y(t) =
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