GOVT 2302 The United States Congress – Constitutional Design.
MAP 2302 Exam #2
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MAP 2302 Exam #2 Name: ____ FJJ loU ID# HONOR CODE: On my honor, I have neither given nor received any aid on this examination. Signature: _ _____ ___________ _ Instru ct ions: Do a ll scratch work on the test its elf. Ma. ke sme your fin a. l answers are clearly labelled . Be sure to simplify all answers whenever possible. SHOW ALL WORK ON THIS EXAM IN ORD ER TO RE CEIVE FULL CREDIT"I No. Score 1 / 16 2 /30 3 /45 4 /9 I Total I /100 I
Transcript of MAP 2302 Exam #2
MAP 2302 Exam #2
Name: _-----,-_K--'~wtr ~f---____
FJJ loUID#
HONOR CODE: On my honor , I have neither given nor received any aid on this examination.
Signature: _ _____ ___________ _
Instructions: Do all scratch work on the test itself. Ma.ke sme your fin a.l answers are clearly labelled . Be sure to simplify all answers whenever possible. SHOW ALL WORK ON THIS EXAM IN ORDER TO RECEIVE FULL CREDIT"I
No. Score 1 / 16 2 /30 3 /45 4 /9
I Total I /100 I
(1) Determine whether the given set of functions is linearly independent on the interval (-00,00). (8 points each)
(a) fl(X) = X, h(x) = x2, h(x) = 4x - 3x2
X X-J. '(\(-lx':l 2)(4-~xW()/'(2./ ~'(_3'(t)= Z" ~-!ok \ _ ....' -::. ~ ~ (~~-ht)
2~ l{-Co)t -(g - (,'l 0 0 Z-
0 7.. -~
(b) JI(x) = eX, h(.1:) = COSX, h(x) = sinx
e.)t Cvr>'IC ~I" :xVI(t'(, to~ Xf ~\~ )c ) -
eX -SfV\ "Ie Qb)c
~y. ~,n)c-MX
=(,X l -Si l\ 'Ie
- to'))c
-=-e\('l\'t\t~ ... ~l~) --LOS 'X fe~Sf'f\)t-e.XC~sX) f-c;,,, >t( - (.J( c.~s); +t~'5i" >t) ~
===-\
(2) Find the general solution of each differential equation. (6 points each)
(a) y(4) - 8y(3) + l 6y" = 0
fY\'4-~~~ -H~r/::-0
~t (-,,'L_~W\ f'fl,) =0
rn1. (rY\ - '1) (~-\{') :;'0
(b) y (4) + l 8y" + 8ly = 0
P' '-i +,~ ~z +~(:::- V
(~~+~) (~2.tG) '=0
iV\'l.-~ =-0 \., ~1.--M =-0
"" - t-3'CI,0, -
(c) y"-6y'+13y=O
~y?-- Cot'h. +r3 -::: Q
t1\ -=- - (~) ±~ {-~y -y (,)(~5 . -= ~:t V3b - S'l.
~(I) ~
~(3:t: 2i-)- - _ ...
-
(d) y" + 3y' - lOy = 0
~y (e) y" + 6y' +j! = 0
~2.+<OMt '1=-0
(~~ 3)(~t'3\:;..a
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(3) Find the general solution of each differential equation. (15 points each)
(a) y" - y' - 6y = 2sin3x
(~-3) (fY\~;}.) =-0
vY\-=- ~I -;).
YI ':: 3Ac.os 3)(. - 3BcslW\3x r
Yrl:: - 'ASi"~)( - qBtbS)x
yi' "'~f' - ~7r :' - 1A~\n 3" - , &eos ~x - (~ACA.,h:- ~~ s\~ ~)c) - ~(As\i\ ~ ~ tBCo~ '3 ~)
-= -q~t~~k- 't&(.05~X - 3A-cos3)c; +-3B~""~x-CoA-sl~~)(-G,6{,os3x ~~ ~
---18"1\ ~ I 0
A- -lQ.. - s:- -:u - - 3~
-,sf t3B~;1- 15t4 -\-3~~.l ~
~s-C- ~ A - ·15"'6 =-0J I-slA t"1ffi -:=o ":}-C(&~ 2
~_--L ~ -=- 'It - 3'\
(b) y" + 9y = 2sec 3x
lA-= c.()~ ~)<.
c{,\A ':- - '3 S\~~xciX
- ~ct\.\:: <:'i~3'1(M
TJ-fA tk ~ ~1__ 1~
Lt.' - ~ 3-x .~ _ 2.
1- 3 3
~,-;: ~ JolJx:: ~ ~
Y= L. CoS 3)( +-C~~jV\ ~)c +- ~ I", \eos ~)C\. Cos h'
+ z."'\.\~I'" ~)c
\ =: ~ I" \M ~ Ie \
(c) y" + 2y' - 3y = 1 + xeX
1" ~ '0' -) :::- 0
fit"L -\- 2m - 3 :::- 0
(VV\~3) (fr\ -I)~ ()
M:: -"), \ -~ 'f..
(C :: ~ e -tC'le
~S : '(r -:: A-\- (eNc.~ ~
J-v:A 6vt5~', 1~ '" IH '( (6~~C.)e~
-= A+ (e,)t+ ex.)t )pl :: (2-~x ~c)eX + (~\/"" ()c)e~
-::.. ( th C2BK\A~C)/ ~; = (1. i1>H (z6t<-))l +("b(2&\{))<~/
:(6)('- -\- (I(e, -I-Lh f (211)-1- 2(~el\
~ • + 'b/ - 3 =(D.../+(~&tI\)c ... ~!,~~,9)e)(If If' IP \~ . ~ .~
-t-2(r-t-~x~\l-)(A+(ti-~)/)
- ~ ~ -x-e'" + (~St~t)e~ -~~ =- 1~ xe J(
~f? = t ~B~ t ~et-\{ c.. -= 0 -cl) ~ +-4. c.. =0 ~C -= -1[P
-3A =: I~ A-=-1 ~f" - ~ t{ 1't'-ii)r\lC
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(4) Set up the appropriate form of a particular solution YP' but do not determine the values of the coefficients. (9 points)
y(5) _ {3) = eX + 2X2 - 5
~ (S) (l)-y =-0
'(r:~ (~2.--,) =-0
'IY\?> (~t ,) (h\ - \) -=- 0
-, ~..4# ~vf.~~;J ~r ~ 1+'1. ~X -I- '(."3 (C,/~D t.t- ~)
Variation
Scratch Paper
