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Unformatted text preview: M ath 341 Section O il: Test #1
This test, has 6 questions on 6 pages. Each question is worth the same. 1. Find the g eneral solution of the differential equation w
J 1 =
— 3*" + C
<3X  ,, (1) L
+C 3^ C v . „ \T 2. Solve t he i nitial value problem
= 5.  =£
2. / ,^ z — ry _ i— 3 3x ^ *^3
T
^
/
I
w
X u = *X / /.
+ C. = 32  2. , 8
OC
T  x 3. Solve the initial value problem
dx at 2
= J, —J, ,
T
T  2. y. (i  ^L u x f 'X f
=» // f c X 0 4. Consider the d ifferential equation
x'V + 2xV  Gy = 0. (1) 4a. Verify t hat each of the f unctions y\ x2 and y<2 = :c~'! is a solution of
the e quation. = ^ =? "  X' 3 4b. Solve tlu; initial value problem consisting of the equation (1) together
with the i nitial conditions y(2) = 10 and y'(1) = 15. 3B
B
8~ 38 , 15
16 ^ nfr i J2B
Jb ~^} _— LL P( = 10 T <Si>
1*0 5=
3 5. Find the general solution of the differential equation f for — T I in — O '• r
9. =0
2. , 2 , 2 ,  2L e
ce 2X K£ ^ c 2 xe 2X 2* e f CB z + t> 6. Consider t he nonhomogeneous differential e quation
y"  7y'+ 12y = Se2*.
6a. Find the "'complementary f unction" (in other words, the general solution
to the corresponding homogeneous equation). r z 7r ^ 3x 6b. Now let's look for a p articular solution. Let's try y = Ae2::'. Can you
find a constant A t hat works?  (\^ ^ u'^At2*
^ 2f\1 = *„,":= >'"2*
u ...
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This note was uploaded on 12/07/2011 for the course MATH 341 taught by Professor Zhang during the Fall '08 term at University of Delaware.
 Fall '08
 Zhang

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