- #1
cloud18
- 8
- 0
y" + 0.5y' + y = 1-cos(t); y(0) = y'(0) = 0
I used method of undetermined coefficients to get particular solution:
Y(t) = -2sin(t) + 1
To get homogeneous solution, I solved characteristic equation to get complex roots:
r_1,2 = -1/4 +- i*sqrt(15)/4
so homogeneous solution is:
y = c1*exp(-1/4*t)cos(sqrt(15)/4*t) + c2*exp(-1/4*t)sin(sqrt(15)/4*t)
But when I use the initial conditions, I get c1 = c2 = 0.
Is this right, or did I make a mistake?
I simplified the original problem with an easier forcing function to try first, so it is possible the ODE doesn't
make sense?
I used method of undetermined coefficients to get particular solution:
Y(t) = -2sin(t) + 1
To get homogeneous solution, I solved characteristic equation to get complex roots:
r_1,2 = -1/4 +- i*sqrt(15)/4
so homogeneous solution is:
y = c1*exp(-1/4*t)cos(sqrt(15)/4*t) + c2*exp(-1/4*t)sin(sqrt(15)/4*t)
But when I use the initial conditions, I get c1 = c2 = 0.
Is this right, or did I make a mistake?
I simplified the original problem with an easier forcing function to try first, so it is possible the ODE doesn't
make sense?