Please see the attached file for the fully formatted problem.
Solve the IVP:
y'' + 4y' +13y = 13t2 -5t +24 +e^-2t(sin 3t)
Please see the attached file for the complete solution.
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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 ...
The expert examines initial value problems solved.