# Initial-Value Problem Solved

Please see the attached file for the fully formatted problem.

Solve the IVP:

y'' + 4y' +13y = 13t2 -5t +24 +e^-2t(sin 3t)

https://brainmass.com/math/numerical-analysis/initial-value-problem-solved-211707

#### Solution Preview

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Solve

Step 1: Find the general solution to the homogenous problem where the RHS is 0.

Let . Then . This has roots . This gives the solution .

Step 2: Find a particular solution to the full problem by using suitable "guesses".

In this case, the guess will look like:

(Note: we need the "t" in front of the last term because the solution to the homogenous ...

#### Solution Summary

The expert examines initial value problems solved.

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