Anish Buchanan

2021-03-07

To determine the solution of the initial value problem

$y{}^{\u2033}+4y=\mathrm{sin}t+{u}_{\pi}\left(t\right)\mathrm{sin}(t-\pi ):$

$y(0)=0,$

${y}^{\prime}(0)=0.$

Also, draw the graphs of the solution and of the forcing function and explain the relation between the solution and the forcing function..

Also, draw the graphs of the solution and of the forcing function and explain the relation between the solution and the forcing function..

Viktor Wiley

Skilled2021-03-08Added 84 answers

Applying the Laplace transform to both sides of the differential equation

By using

Using the initial conditions,

By using the partial fraction

Applying the inverse Laplace transformation on both sides,

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