math problem
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′′(x) − 3y′(x) + 2y(x) = ex sin(x)
2. Find a general solution to the differential equation.
y′′(θ) + 2y′(θ) + 2y(θ) = e−θ cos(θ)
3. Find the solution to the initial value problem.
y′′(θ) − y(θ) = sin(θ) − e2θ, y(0) = 1, y′(0) = −1
4. Find a general solution to the differential equation using the method of variation of
parameters.
y′′ + 2y′ + y = e−t
5. Find a general solution to the differential equation using the method of variation of
parameters.
y′′ + 9y = sec2(3t)
6. Find a general solution to the differential equation using the method of variation of
parameters.
y′′ + 4y′ + 4y = e−2t ln(t)
7. Find a general solution to the differential equation to the given Cauchy-Euler equation
for t > 0. d2w
dt2 +
6
t
dw
dt +
4
t2 w = 0
8. Find a general solution to the differential equation to the given Cauchy-Euler equation
for t > 0.
9t2y′′(t) + 15ty′(t) + y(t) = 0
9. Find a general solution to the differential equation to the given Cauchy-Euler equation
for t < 0.
y′′(t) − 1
t y′(t) +
5
t2 y(t) = 0
10. Find a general solution to the differential equation to the given Cauchy-Euler equation
for t < 0.
t2y′′(t) + 9ty′(t) + 17y(t) = 0
11. Solve the given initial value problem for the Cauchy-Euler equation.
t2y′′(t) − 4ty′(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′′′ + 3y′′ + 28y′ + 26y = 0
13. Find a general solution to the differential equation with x as the independent variable.
y(4) + 4y′′′ + 6y′′ + 4y′ + 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′′′(x) − y′′(x) − 4y′(x) + 4y(x) = 0; y(0) = −4 , y′(0) = −1 , y′′(0) = −19
16. Solve the given initial value problem.
y′′′(x) − 4y′′(x) + 7y′(x) − 6y(x) = 0; y(0) = 1 , y′(0) = 0 , y′′(0) = 0
17. Use the annihilator method to determine the form of a particular solution for the given
equation.
y′′ + 2y′ + 2y = e−x cos(x) + x2
18. Use the annihilator method to determine the form of a particular solution for the given
equation.
z′′′ − 2z′′ + z = x − ex
19. Use the method of variation of parameters to determine a particular solution to the
given equation.
z′′′ + 3z′′ − 4z = e2x
20. Use the method of variation of parameters to determine a particular solution to the
given equation.
y′′′ + y′′ = tan(x), 0 < x < π 2