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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{f(t)} and n = 1, 2, 3,..., then L{t"(t)} = (-1)^_ F(s). 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) and then find y(t) = L-{Y(s)}. ty" – y' = 4t2, y(0) = 0 y(t) =

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{f(t)} and n = 1, 2, 3,..., then L{t"(t)} = (-1)^_ F(s). 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) and then find y(t) = L-{Y(s)}. ty" – y' = 4t2, y(0) = 0 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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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{f(t)} and n = 1, 2, 3,..., then L{t"f(t)} = (-1)"º F(s). ds" 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) and then find y(t) = L{Y(s)}. ty" – y' = 4t2, y(0) = 0 y(t) =
Transcribed Image Text: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{f(t)} and n = 1, 2, 3,..., then L{t"f(t)} = (-1)"º F(s). ds" 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) and then find y(t) = L{Y(s)}. ty" – y' = 4t2, y(0) = 0 y(t) =
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