Question 212136
Let x=e^(rt), x'=r*x, x''=r^2*x
x"+2x'+2x=0
r^2*x+2r*x+2x=0
r^2+2r+2=0
Using the quadratic formula,
r=-1+/-i
x=e^((-1+/i)t)
x=e^(-t)*(C1*cos(t)+C2*sin(t)), where C1 and C2 are constants.