consider the equation

d^2(x)/dt^2= h(t)+9x

First suppose that h(t)= 4e^-3t

1) write down the derive command to find the general solution of equation with h(t)= 4e^-3t. hence write down the general solution of equation.

2)A student solve this equation using CF/PI find the general solution is

x(t)=Ae^3t + Be^-3t + 6te^-3t. assuming that your answer in part 1 is correct, determine by any suitable means whethe the student's answer is correct.

3) find the particular solution which also satisfies the initial conditions x(0)=12 and x(0)=0