Question
Asked Feb 27, 2020
191 views

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)

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Expert Answer

Step 1

We are given the differential equation by

                                     Advanced Math homework question answer, step 1, image 1.

Advanced Math homework question answer, step 1, image 2

So, first, we will solve for yh and then yp.

         Advanced Math homework question answer, step 1, image 3

Step 2

Now, the particular solution.

                Advanced Math homework question answer, step 2, image 1

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

                               Advanced Math homework question answer, step 2, image 2.

 

...

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