1.Find the form of the particular solution to each ODE below.

Do not solve for the constants in the particular solution.

a) y"+4y=3t^(2)*e^(9t)*cos(5t)

b) y"-4y'+4y=t*e^(2t)+t

2. If a mass-spring system is underdamped and modeled with the IVP

x" + x' + x = 0, x(0) = 1 ,x'(0) = 1

then the solution of the ODE predicts that the mass will pass

through the equilibrium position infinitely many times

3. If x(t) = -cos(t)- sin(t) represents the position of a mass on a spring,

then the phase is equal to pi/4

.