Exercise: Solving an IVP Problem with Laplace Transforms: Difference between revisions
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Latest revision as of 00:36, 29 January 2010
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.
References
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