Math 2552 — Differential Equations Worksheet 21 (Apr 1, Review)
Georgia Institute of Technology, Spring 2019 Review for exam 2
1. Chapter 4:
a. Solve the IVP: y00 + 6y0+ 3y= 0; y(0) = 1 y0(0) = 0
b. Solve the ODE using the method of undetermined coefficients:
y00 −2y0−3y=−3te−t
c. Solve the ODE using variation of parameters:
y00 + 4y0+ 4y=t−2e−2t
2. Chapter 5:
a. Solve the IVP using the method of Laplace Transforms:
y00 −2y0+ 2y= cos t;y(0) = 1, y0(0) = 0
b. Find the Laplace transform of:
f(t) =
t20≤t < 2
2 2 ≤t < 6
cos t6≤t < 10
0otherwise
c. Find the inverse Laplace transform:
F(s) = e−s+e−2s−e−3s−e−4s
s
d. Find the inverse Laplace transform:
F(s) = se−s
s2−2s+ 10
1
