Question

Asked Feb 27, 2020

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Consider the initial value problem: y′′+16y=e^-t, y(0)= y_0, y′(0)=y'_0

Suppose we know that y(t)→0y as t→∞. Determine the solution and the initial conditions.

Find:

y(t)

y(0)

y'(0)

Step 1

We are given the differential equation by

.

So, first, we will solve for y_{h} and then y_{p}.

Step 2

Now, the particular solution.

So, the solution of the given differential equation is given by,

.

...

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