y" + 0.5y' + y = 1-cos(t); y(0) = y'(0) = 0(adsbygoogle = window.adsbygoogle || []).push({});

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?

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Method of undetermined coefficients

**Physics Forums | Science Articles, Homework Help, Discussion**