- #1
shamieh
- 539
- 0
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$
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$