- #1
eric2921
- 8
- 0
Homework Statement
d^3x/dt^3 - d^2x/dt^2 = 3e^t - sin(t)
Homework Equations
not sure. maybe sin(t)=.5*i*e^(-i*t)-.5*i*e^(i*t)
The Attempt at a Solution
I'm pretty sure we start by finding the complementary solution by setting the right side equal to 0. So we have:
D^3 x - D^2 x = 0
D^2 [D-1] x = 0
then we solve for D and get 0, 0 and 1 for solutions.
this gives us:
xcomp. = [c1+t c2] e^(0t) + c3 e^t
xcomp. = c1 + c2 t + c3 e^t
now its my understanding that i need to find particular solution because:
x = xcomp. + xpart.
So i was told that the solutions to the particular solution are 1, i and -i. I don't understand why that is though but if that's the case then i think:
xpart. = t e^t + A cos(t) + B cos(t)
and
x= c1 + c2 t + c3 e^t + t e^t + A cos(t) + B cos(t)
I'm stuck here, I'm pretty sure it's correct up to this point although i could be wrong. I don't know to find A or B though which i think all i have left to do. Thanks for any help!