Exercise: Solving an IVP Problem with Laplace Transforms

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Author

John Hawkins

Problem Statement

Solve the following initial value problem using Laplace Transforms:


Note: This problem was solved by Zill without the use of Laplace Transforms.<ref>Dennis G. Zill, A first course in Differential Equations, 8th ed., Int. ed (Belmont, CA: Thomson Learning, 2005), 128.</ref>

Solution

Given the initial ODE


we take the Laplace transform of both sides


Using the transforms displayed in Laplace Transform, we find this to be


which, with initial values substituted, gives


Hence,




Using a calculator to expand this, we have



And therefore, using the equations on Laplace Transform to perform an inverse Laplace transform, we have our solution:


This equation matches that found by Zill, providing confirmation of a correct solution.

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