Mathematics homework help. MATH 275 TEST 2 REVIEW
INSTRUCTIONS : REDUCE / SIMPLIFY ALL ANSWERS AND KEEP ALL
EXPONENTS POSITIVE WHERE APPLICABLE.
1. Find a general solution to the differential equation.
y
00(x) − 3y
(x) + 2y(x) = e
x
sin(x)
2. Find a general solution to the differential equation.
y
00(θ) + 2y
(θ) + 2y(θ) = e
−θ
cos(θ)
3. Find the solution to the initial value problem.
y
00(θ) − y(θ) = sin(θ) − e

, y(0) = 1, y
(0) = −1
4. Find a general solution to the differential equation using the method of variation of
parameters.
y
00 + 2y
0 + y = e
−t
5. Find a general solution to the differential equation using the method of variation of
parameters.
y
00 + 9y = sec2
(3t)
6. Find a general solution to the differential equation using the method of variation of
parameters.
y
00 + 4y
0 + 4y = e
−2t
ln(t)
7. Find a general solution to the differential equation to the given Cauchy-Euler equation
for t > 0.
d
2w
dt2
+
6
t
dw
dt +
4
t
2
w = 0
8. Find a general solution to the differential equation to the given Cauchy-Euler equation
for t > 0.
9t
2
y
00(t) + 15ty0
(t) + y(t) = 0
9. Find a general solution to the differential equation to the given Cauchy-Euler equation
for t < 0.
y
00(t) −
1
t
y
(t) + 5
t
2
y(t) = 0
10. Find a general solution to the differential equation to the given Cauchy-Euler equation
for t < 0.
t
2
y
00(t) + 9ty0
(t) + 17y(t) = 0
11. Solve the given initial value problem for the Cauchy-Euler equation.
t
2
y
00(t) − 4ty0
(t) + 4y(t) = 0; y(1) = −2 , y
(1) = −11
12. Find a general solution to the differential equation with x as the independent variable.
y
000 + 3y
00 + 28y
0 + 26y = 0
13. Find a general solution to the differential equation with x as the independent variable.
y
(4) + 4y
000 + 6y
00 + 4y
0 + y = 0
14. Find a general solution to the given homogeneous equation.
(D + 4)(D − 3)(D + 2)3
(D2 + 4D + 5)2D5
[y] = 0
15. Solve the given initial value problem.
y
000(x) − y
00(x) − 4y
(x) + 4y(x) = 0; y(0) = −4 , y
(0) = −1 , y
00(0) = −19
16. Solve the given initial value problem.
y
000(x) − 4y
00(x) + 7y
(x) − 6y(x) = 0; y(0) = 1 , y
(0) = 0 , y
00(0) = 0
17. Use the annihilator method to determine the form of a particular solution for the given
equation.
y
00 + 2y
0 + 2y = e
−x
cos(x) + x
2
18. Use the annihilator method to determine the form of a particular solution for the given
equation.
z
000 − 2z
00 + z = x − e
x
19. Use the method of variation of parameters to determine a particular solution to the
given equation.
z
000 + 3z
00 − 4z = e
2x
20. Use the method of variation of parameters to determine a particular solution to the
given equation.
y
000 + y
00 = tan(x), 0 < x < π
2

Mathematics homework help