# Initial-Value Problem with Graph : Laplace Tranformations and Partial Fractions

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For t>0, let F(t) be the Phi-periodic function which on [0,pi] has the graph attached to this problem.

a) Solve the IVP

y"+4y=F(t)

y(0)=0=y'(0)

b) Graph the solution on the interval [0,3pi]

c) Discuss the behavoir of the solution in relation to the equation.

For the solution please use Laplace transformations and partial fractions.

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#### Solution Summary

An IVP is solved using a graph, an inverse laplace transformation, and partial fractions. The solution is graphed and discussed. The solution is detailed and well presented.

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