 
Summary: Math 5A: Review Sheet
1. Review all previous homework assignments.
2. For each problem below, know how to (1) find the general solution to the associated homogeneous equa
tion, (2) find a particular solution to the nonhomogeneous equation, (2) find the general solution to the
nonhomogeneous equation, and (4) solve the initial value problem.
(a) y + 4y + 4y = 4te3t
, y(0) = 1, y (0) = 2,
(b) y + 2y + y = 3 cos(t), y(0) = 1, y (0) = 2,
(c) y + 16y = cos(4t), y(0) = 1, y (0) = 1,
(d) y  4y + 3y = et
+ 2e5t
, y(0) = 0, y (0) = 0,
(e) y + 4y + 4y = t3/2
e2t
, y(0) = 0, y (0) = 4,
(f) y + y = cot(t), y(/4) = 0, y (/4) = 1.
3. (a) By setting y = tr
as a trial solution, find the general solution to the differential equation t2
y 2ty +
2y = 0, t > 0.
