Department of Mathematics
Differential Equations – Math 331
Homework 4
1. Find
(i) Laplace transform of f(t) = tetsin(2t)
(ii) fπ
2if f(t) = 2t+u1(t)(tsint) + u3(t)(tcos2t).
2. Find
(i) (1∗1)∗1.
(ii) the solution of the integral equation φ(t) +
t
R
0
(t−u)φ(u)du=1
3. Solve the IVP: y00 +4y=δ(t−π),y(0) = 1, y0(0) = 0.
4. Solve the following system using Laplace Transform
f0(t) = f(t) + 2g(t),f(0) = 1
g0(t) = 2f(t) + 4g(t),g(0) = 3
5. Find the two fundamental solutions for the linear system
x0=3−2
2−2x, ~x=5
4.
6. Solve the linear system
x0=2 9
−1−4x.
7. Find
(i) 1 ∗δ(t−1) =
(ii) Laplace transform of r(t) = t u3(t)et−3.
