In recording an earthquake, the response of the accelerogram is governed by the differential equation
x'' + 2nwx' + w^2x = -a(t)
where x(t) is the instrument response recorded on the accelerogram, a(t) is the ground acceleration, n is the damping ratio of the instrument, and w is the undamped natural frequency of the instrument. Take n=w=1 and a(t)=e^-t/(1+t)^2 and find the general solution of this differential equation.