Math 244 Midterm Exam 1 10/13/09 Mike Robertson Section: Name: Instructions.No notes or calculators allowed on this exam. Please turn o your phones. This exam is worth 200 points. If improvement is shown at the nal exam, your score will be raised. Point v
1.1 Differential Equations: Derive and substitute to verify
1.2
Make sure to check the domain!
1.3
Use implicit derivation when possible (2y)y' +2x
1.4 Separable Variable Equations
TYPE: y = f(x)g(y)
Step 1: Separate
Step 2: Integrate
Step 3: Solve for Y
1
Solutions to Section 1.1
TrueFalse Review:
1. FALSE. A derivative must involve some derivative of the function y = f (x), not necessarily the rst
derivative.
2. TRUE. The initial conditions accompanying a dierential equation consist of the values of y,
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February 14, 2017 ~
Math 244
Group Quiz on Sections 4.3 & 4.4
Winter 2017
Group number and a name for your group
This is a closed book, closed notes quiz.
In order to receive maximal credit, show or justify all work!
x
1. [6] Let W =
2 R2 : x y .
y
(a) Is
Math 241 EXAM I Name K ng
Unless otherwise stated, each part of each problem is worth 6
points. For partial credit consideration, show wOrk.
1. Consider the 2dcontour map of   .31
f (2:, y)_ sketched on the right. ' '
(a) Is Daf(P) positiire, negative,
_ 3
1. [10 pts.] Solve the initial value problem: % = 4:+ 5:, y(0)=1.
4g , 4x~x y
on  4+93
(4433)% 1: 41*?!3
J(H+HZ)%M 436
I4 '
4g+r=27 KMT
4. 22L
13(o)=l HUN :4 'ZLO) LI
min
1? ,
7:0
Jilli = 1,291 + H
H 44 2'" u T
W. M.
2 [5pts.] Determine all value
M
(9 pts) 1. Decide if the statement is true or false. In order to receive full credit, justify your
answer.
(a) If A and B are both 2 x2" matrices, then AB : BA.
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A B A B _
0 \ l O _ O 9 AB =* O a V
[ O 0 O b 0 C) D
O ,
4% 0'w 0A 3' EA l BA: [(3
Quiz 4 Math 244 Wi 05 Name u t  .4 . _ a.
Show all work for full credit.
1.)(10)Given one solution for the following D.E., find a general solution.
9y<3>+11y<2)+4y<14y=0; y1=e'xsinx
m3 +Hr + w am
(Qr 73
/(z+2r*2.5m «1*2+2:O
.. (Wh \w Mfr)

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ki k/
Quiz 1 Math 244 Wi 05 Name
Show work for full credit. No calculators are to be used on this quiz.
l.)(lO)Solve the following separable D.E.:
y+y2=y
d/ 3
"Z: '0
t, . v; I 1
Ca («~33 :Céjci
("l +ch\\1': Cex
< f , 2.). £10)Show that the fol
(9 pts) 1. Decide if the statement is true or false. In order to receive full credit, justify your
answer. Justication counts more than the correct choice of true or false.
(a) A set of three vectors in a vector space are linearly dependent if and only if