In: Advanced Math
Use the method of undetermined coefficients (it works the same way for a fourth order linear equation) to find the general solution of:
y(4) - 18y'' + 81y = 6t2 - 4t + 36 + 90e3t
[Hint: The complementary solution is yc = C1e3t + C2e-3t + C3te3t + C4te-3t