# The solution of the initial value problem y'' + 4y=2delta(t - pi/4), y(0)=0, y'(0)=0 and draw the graph of the solution.

The solution of the initial value problem and draw the graph of the solution.
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Delorenzoz

Let the differential equation
Applying the Laplace transform to the differential equation,

By using and

Using the initial conditios

Now, applying the inverse Laplace transformation on both sides,

By using and properties of inverse Laplace,

Therefore, the solution of the initial value problem
is

By using
For
For
Thuse, the graph of the solution is as below: