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

2θ

, 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