Download MATH 308 Homework 12

Texas A&M University
Department of Mathematics
Volodymyr Nekrashevych
Fall 2010
MATH 308 Homework 12
12.1. Solve the equation y 0 = x(x2 + 1)/4y 3 .
12.2. Solve the initial value problem
−2 1
0
x =
x,
−5 4
x(0) =
12.3. Solve the initial value problem
3
−2
0
4
x =
x,
1 − 54
x(0) =
1
1
1
0
.
.
12.4. Solve the initial value problem
y 00 + 9y = sin 3t,
y(0) = 1,
y 0 (0) = 0.
12.5. Find the inverse Laplace transform of the function
1
.
2
(s + 1)(s + 2s + 2)
12.6. Use the Laplace transform to solve the initial value problem
y 00 + 4y + 4 = e−2t + sin t,
y(0) = 0,
y 0 (0) = 0.
y(0) = 0,
y 0 (0) = 1.
12.7. Find solution of the initial value problem.
y 00 + 4y = δ(t − 2) + sin 2t,
12.8. Find the general solution of the system


1 1 2
x0 =  1 2 1  x.
2 1 1
12.9. Find the general solution of the system


2 1 3
x0 =  0 0 1  x.
0 −1 0
12.10. Find eAt if
A=
−2 1
−5 4
.