# Solve a 2nd order ODE.

Use methods of undetermined coefficients to find one solution of:

y'' + 2y' +2y =

(10t+7)e^(-t)cos(t)+(11t+25)e^(-t)sin(t)

https://brainmass.com/math/ordinary-differential-equations/solve-2nd-order-ode-27369

#### Solution Preview

First the homogenous solution. The charac. equation is r^2+2r+2=0 which gives us:

r= -1+i and r= -1-i, then yh= c1exp(-t)cos(t)+ c2exp(-t)sin(t).

Now in this case the guess for the particular solution is yp= (at+b)exp(-t)cos(t)+ ...

#### Solution Summary

A 2nd order ODE is solved. The solution is detailed.

$2.19