1. Use the method of undetermined coefficients to find the general solution to the ODE.

y"-7y=2t^2-14t-e^(7t)

2.Use the method of undetermined coefficients to find the general solution to the ODE.

y"-4y'-5y=3cos(2t)+te^(2t)

3.A mass weighing 20 N is tied a spring hanging from the ceiling, and stretches the

spring 5 m. The damping force is numerically equal to 6 times the instantaneous velocity, at

all times. Suppose the mass is set in motion by compressing the spring 2m, and releasing it

with no initial velocity. Use g = 10 m=s^2 for gravitational acceleration.

a) Write the ODE with initial conditions modelling the position of the mass at any time t (you

may assume t 0).

b)Solve the ODE from part a

C) How high up does the mass ever go?

D) How far down does this mass ever go?