MHB Is My Work Correct for These Particular Solutions?

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shamieh
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I just need someone to verify that my work is correct.

Note that the general solution to $y'' - y = 0$ is $y_h = C_1e^t + C_2e^{-t}$

In the following, use the Method of Undetermined Coefficients to find a particular solution.
b) $y'' - y = 4sint + 2cost$

Solution:
$y_p = -cost - 2sint$
c)$y'' - y = e^t$

Solution:
$y_p = \frac{1}{2} te^t$

d) Give a particular solution to $y'' - y = t^2 + 4sint + 2cost + e^t$

Solution:
$ y_p = -t^2-2 -cost - 2sint + \frac{1}{2}te^t$
 
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Yes, that's correct. (Yes)
 
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