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Final
You scored 60 out of 130
Question 1
Your answer is CORRECT.
Give the differential equation that has as its general solution.
a)
b)
c)
d)
e)
f) None of the above.
Question 2
Your answer is CORRECT.
Give the general solution of.
a)
b)
c)
d)
e)
y = C 1 +C 2 e^3 x
y ′ − 3y = 0
y ′′^ − 3 y ′= 0
y ′′^ + 3 y ′= 0
y ′′^ − 9 y ′= 0
y ′ − 9y = 0
x y′^ + 5y =
3 e−4^ x x^4
y = (− ) + C
e−4^ x
y = (− )^ +
3 x^5 4
e−4^ x^
C
x^5
y = (− ) +
4 x^5
e−4^ x^
C
x^5
y = ( ) +
x^5
e−4^ x^
C
x^5
y = (− ) +
4 x^4
e−4^ x^
C
x^4
f) None of the above.
Question 3
Your answer is INCORRECT.
Give the general solution of.
a)
b)
c)
d)
e)
f) None of the above.
Question 4
Your answer is CORRECT.
Give the general solution to
a)
b)
c)
d)
e)
f) None of the above.
Question 5
Your answer is CORRECT.
The function is a solution of second order linear homogeneous differential equation with constant coefficients. The differential equation is:
y′^ =
xy − 2y y^2 + 4
y^2 + 8 ln(y) = x^2 − 4 x + C
y^2 − 16 ln(y) = −2 x^2 + 8 x + C
y^2 + 4 ln(y) = −1/2 x^2 + 2 x + C
y^2 + 8 ln(y) = x^3 − 4 x^2 + C
y^2 + 4 ln(y) = −2 ln(y)x − 32 x + C
y′′^ + 2 y′+ 5y = 0
y = C 1 e−x^ + C 2 xe−x
y = C 1 ex^ cos(2 x) + C 2 exsin(2 x)
y = C 1 ex^ +C 2 e−2^ x
y = C 1 e−x^ cos(2 x) + C 2 e−xsin(2 x)
y = C 1 e−x^ +C 2 e^2 x
y = e^3 xcos(4x)
d)
e)
f) None of the above.
Question 8
Your answer is INCORRECT.
Give the form of a particular solution to
a)
b)
c)
d)
e)
f) None of the above.
Question 9
Your answer is CORRECT.
Give the Laplace transform of the solution to.
a)
b)
c)
d)
e)
{ e−3^ x^ , e−3^ x^ cos(4 x), e−3^ xsin(4 x)}
{ e−3^ x^ , e^3 x^ cos(4 x), e^3 xsin(4 x)}
y′′′^ − 16 y′^ = 4 e^4 x− 4 cos(4 x) − 3
z = Ax e^4 x+ B cos(4 x) + C sin(4 x) + Dx + E
z = A e^4 x+ Bx cos(4 x) + Cx sin(4 x) + Dx
z = Ax e^4 x+ B cos(4 x) + C sin(4 x) + D
z = A e^4 x+ B cos(4 x) + C sin(4 x) + Dx
z = Ax e^4 x+ B cos(4 x) + C sin(4 x) + Dx
y′′^ − 2 y′^ − 3y = 1 with y(0) = 2 and y′(0) = 0
Y (s) = +
s(s + 1)(s − 3)
2 s − 4 (s + 1)(s − 3)
Y (s) = −
s(s + 1)(s − 3)
(s + 1)(s − 3)
Y (s) = +
s(s + 1)(s − 3)
2 s (s + 1)(s − 3)
Y (s) = +
s(s + 1)(s − 3)
4 − 2 s (s + 1)(s − 3)
Y (s) = −
s(s + 1)(s − 3)
2 s + 4 (s + 1)(s − 3)
f) None of the above.
Question 10
Your answer is INCORRECT.
Give the Laplace transform of
a)
b)
c)
d)
e)
f) None of the above.
Question 11
Your answer is INCORRECT.
Give the inverse Laplace transform of
a)
b)
c)
f(x) = { 5 x x^2
0 ≤ x < 2 x ≥ 2
F (s) = − + − 6
s^2
e−2^ s^
s^3
e−2^ s^
s^2
e−2^ s^
s
F (s) = + − − 6
s^2
e−2^ s^
s^3
e−2^ s^
s^2
e−2^ s^
s
F (s) = + + 9 + 14
s^2
e−2^ s^
s^3
e−2^ s^
s^2
e−2^ s^
s
F (s) = + + 9 − 6
s^2
e−2^ s^
s^3
e−2^ s^
s^2
e−2^ s^
s
F (s) = + + + 6
s^2
e−2^ s^
s^3
e−2^ s^
s^2
e−2^ s^
s
F (s) = + − −
s
s^2
e−2^ s s^2
3 e−2^ s s + 4
f(x) = { 4 − 4x −5 x + 4 − 3 e−4 (x−2)
0 ≤ x < 2 x ≥ 2
f(x) = {
4 − 4x −5 x + 6 − 3 e−4 (x−2)
0 ≤ x < 2 x ≥ 2
f(x) = { 4 − 4x −5 x + 6 − 3 e−4^ x
0 ≤ x < 2 x ≥ 2
b)
c)
d)
e)
f) None of the above.
Question 14
Your answer is INCORRECT.
This is a written question, worth 12 points. DO NOT place the problem code on the answer sheet. A proctor will fill this out after exam submission. Show all steps/work on your answer sheet for full credit. Problem Code: 1424
Given the differential equation:
(a) Identify the equation (i.e., linear, separable, Bernoulli, homogeneous). (b) Find the general solution. (c) Find the solution satisfying
a) I have placed my work and my answer on my answer sheet.
b) I want to have points deducted from my test for not working this problem.
Question 15
Your answer is INCORRECT.
x^2 y′^ = 4 x^3 y^3 + xy
y(1) = 2.
This is a written question, worth 12 points. DO NOT place the problem code on the answer sheet. A proctor will fill this out after exam submission. Show all steps/work on your answer sheet for full credit. Problem Code: 1555
A disease is spreading through a herd of 200 goats. Let be the number of goats who have the disease days after the outbreak. The disease is spreading at a rate proportional to the number of goats who do not have the disease. Suppose that 20 goats had the disease initially and 50 goats have the disease after 2 weeks.
(a) Give the mathematical model (initial value problem) for. (b) Find the general solution of the differential equation in (a). (c) Find the particular solution that satisfies the given conditions.
a) I have placed my work and my answer on my answer sheet.
b) I want to have points deducted from my test for not working this problem.
Question 16
Your answer is INCORRECT.
This is a written question, worth 12 points. DO NOT place the problem code on the answer sheet. A proctor will fill this out after exam submission. Show all steps/work on your answer sheet for full credit. Problem Code: 1655
is a solution of the reduced equation of
(a) A second solution of the reduced equation has the form. Find and show that form a fundamental set of solutions of the reduced equation. (b) Find a particular solution of the given equation. (c) Find the general solution of the given equation.
a) I have placed my work and my answer on my answer sheet.
b) I want to have points deducted from my test for not working this problem.
Question 17
Your answer is INCORRECT.
This is a written question, worth 12 points. DO NOT place the problem code on the answer sheet. A proctor will fill this out after exam submission. Show all steps (work) on your answer sheet for full credit. Problem Code: 1723 Given the initial value problem. (a) Find the Laplace transform of the solution.
G(t) t
G
y 1 = x
y′′^ − + y =
x
y′^
x^2
x
y 2 =xr^ y 2 { y 1 , y 2 }
y′ − 4y = 5 sin(2x), y(0) = 3
b) I want to have points deducted from my test for not working this problem.
