N ame:
M a t h 3 36-4, F all 2 013, Q uiz 4
P rof. Ammar
S how y our w ork!
1 . C onsider t he d ifferential equation
'+
V
xj
dx + [y^ + I n x)dy = 0.
(a) Use the p artial derivatives t est t o show that this differential equation is e xact.
M/^.^)^
^'+-1
MATH 3364
Prof. Ammar
Answers to Exam 2
Fall 2013
1. For any nonzero number k , we get the vanishing nontrivial linear combination (2k )f (x)+
(3k/5)g (x) + (k )h(x) 0.
2. (a) Two steps of Eulers method yields y (2) y2 = 6.
(b) Two steps of the Improved E
MATH 3364
Prof. Ammar
1. yp (x) =
Answers to Exam 3
Fall 2013
4 3/2 2x
xe
3
3
9
cos 3t +
sin 3t = C cos(t ), where C = 3 10/40, = 3, and
40
40
= + tan1 (3) 1.89255.
2. xsp (t) =
3. (a) f (t) = e3t 2 cos 4t +
(b) f (t) =
5
sin 4t
4
1
1
cos 2t
cos 4t
12
1
MATH 336
Answers to Spring 2008 Final Exam
1. y (x) = 4e2x 3e2x .
2. (a) The general solution is y (x) = 4+1/(C 14e5x )1/7 . Also, y (x) 4
is a singular solution.
(b) x2 ey + y cos x + y 5 = C .
(c) y 2 2xy + 3x2 = C .
(d) y (x) = c1 ex + c2 + c3 x + 18/7
MATH 336
Final Exam
Spring 2009
Name:
Student (Z) Number:
Signature:
There are 200 total points possible. You must show your work and justify your answers
to receive credit. Clearly indicate your answers by circling them.
1. (15 pts.) Determine the soluti
1
MATH 336
Answers to Fall 2012 Final Exam
A1. y (x) =
3
1
+ x2
x
8
A2. y (x) =
4
3 + cos 4x
A3. x2 y 1 + ye2x x +
13
y =C
3
A4. y (x) = x Cx2 1
A5. y (x) = c1 e3x + c2 ex
1
2
cos 3x sin 3x
3
3
A6. y (x) = c1 e2x + c2 e4x +
1 x 1 2x
e + xe
15
2
A7. yp (x
MATH 336
Final Exam
Fall 2012
Part A: Do any 8 of the following 10 problems.
A1. Determine the solution y (x) of the initial-value problem
x2 y 2xy = 3,
y (2) = 1.
A2. Find the solution y (x) of the initial-value problem
dy
= y 2 sin 4x,
dx
y (0) = 1
A3.
MATH 336
1. y (x) =
Answers to Spring 2009 Final Exam
3
4 e3x
1
2
2. y (x) = (x 1) + (x 1)2
3
3
1
3. (a) 2x2 y 1/2 + x3 4x1/2 y 1/2 + y 2 = C
3
(b) y (x) = x C x4 (1/2)
4. y (x) = c1 cos 2x + c2 sin 2x + c3 e
5. y (x) = c1 cos 2x + c2 sin 2x +
2x
+ c 4 e
MATH 336
Spring 2010 Final Exam
1. (16 pts.) Determine the solution y (x) of the initial value problem xy 3y = x2 , y (1) = 2.
2. (16 pts.) Find the solution y (x) of the initial value problem (x2 + 1)y = xy 2 , y (0) = 4.
3. (16 pts. each) Find the gener
M a t h 3 3 6 - 4 , F a l l 2013,
Quiz 2
^oluhi'^
Name:
P rof. A m m a r
Show your w o r k !
1 . F ind the particular solution ycfw_x)
ij'
So
o f the i nitial v alue problem
+ 2xy =
X,
ycfw_0) =
i
-2.
MATH 3364
Prof. Ammar
Answers to Exam 1
1. (linear) y (x) = x5 + 3x3
2. (separable) y (x) =
3
3 ln |3x + 1|
3. (homogeneous, and also Bernoulli) y (x) = x
4. (a) Show that My = Nx =
(b) 2x1/2 y 1/2 + xy 2 + x +
1 1/2 1/2
x
y
+ 2y
2
12
y =C
2
5. (Bernoulli