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the ential equation 2y" + ty'- 2y 14, y(0) = y'(0) = 0. n some instances, the Laplace transform can be used to solve linear differential equations with variable mono THEOREM 7.4.1 Derivatives of Transforms If F(s) = L{f(t)} and n = 1, 2, 3, ..., then Left)} = (-1)"_5), ds" to reduce the given differential equation to a linear first-order DE in the transformed function Y(s) = L{y(t)}. Solve the first-order DE for Y(s). Y(s) =

the ential equation 2y" + ty'- 2y 14, y(0) = y'(0) = 0. n some instances, the Laplace transform can be used to solve linear differential equations with variable mono THEOREM 7.4.1 Derivatives of Transforms If F(s) = L{f(t)} and n = 1, 2, 3, ..., then Left)} = (-1)"_5), ds" to reduce the given differential equation to a linear first-order DE in the transformed function Y(s) = L{y(t)}. Solve the first-order DE for Y(s). Y(s) =

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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Consider the differential equation 2y"+ ty'-2y = 14, y(0) = y'(0) = 0. In some instances, the Laplace transform can be used to solve linear differential equations with variable monomial coefficients. Use Theorem 7.4.1., THEOREM 7.4.1 Derivatives of Transforms If F(s) = L{ft)} and n = 1, 2, 3,..., then L{"{t} = (-1)F(s), ds" to reduce the given differential equation to a linear first-order DE in the transformed function Ys) = Lly(t)}. Solve the first-order DE for Y(s). Y(s) =| Then find y(t) = Z (Y(s)}. y(t)%D
Transcribed Image Text:Consider the differential equation 2y"+ ty'-2y = 14, y(0) = y'(0) = 0. In some instances, the Laplace transform can be used to solve linear differential equations with variable monomial coefficients. Use Theorem 7.4.1., THEOREM 7.4.1 Derivatives of Transforms If F(s) = L{ft)} and n = 1, 2, 3,..., then L{"{t} = (-1)F(s), ds" to reduce the given differential equation to a linear first-order DE in the transformed function Ys) = Lly(t)}. Solve the first-order DE for Y(s). Y(s) =| Then find y(t) = Z (Y(s)}. y(t)%D
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