This preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: Math 252 Exam 1 February 28, 2008 Musial Musial Name—______—
Instructions. Work each problem on the exam.. Where you are asked to solve an equation,
make sure to ﬁnd all solutions. Show all work. 1. Solve the DE. j—Z=1+$+y+$y.
% : My +7(/47(]
M My
jJ/M "3 "w '3 *C 2
)  s'X'JrlgL'FC 79+ X2
kl Jr a  Q < )< 6.
gal: 2. Solve the DE and give the largest intervals on which a solution can exist: 937/ + 2y = 3x .’ L 5 ,
51%;?”3 7640 withg
_ Q
7> 7” >21 3. A tank initially contains 300 gallons of saline solution with salinity 6 lbs of salt per
gallon of solution. Solution having salinity 4 lbs of salt per gallon is pumped into the
tank at a rate of 2 gallons per minute, and solution leaves the tank at the same rate
of 2 gallons per minute. Find the function A (t) which models the amount of salt in
the tank at any time, and ﬁnd the amount if salt in the tank after a long time. 21 gay/M) L; lei/gig
I/H 4. The number of students at a college which have been exposed to an inﬂuenza virus is modelled by the DE
d2:
E _. km (2000 — x) where a: is the number of students exposed after t days. On day 0, 1 student has been
exposed, on day 6, 15 students have been exposed. Solve for k.. W $0000» "X2 ZKVH’ W \ ,
/—+——~— : _‘—« .1 . 1
7C ( 1000 ' X) 209° 74' A + goo / e
“ :wwﬁx +A/waaY)/
1 fowJA/Y/W.—>c)) So
A %{0(‘/ma~>) .: 14 +c
3.00)
0+ éw/ ‘ 0+ += 6, ngo/Qq(("ﬁqq] : C J— /Qh(/S lag?) 200 0 049038 f, GK +5003g K: O. 000 125/ 5. Verify that the following differential form is exact and solve it. Note that — arctan y = dy $+y (m+arctany)d$+1+y2dy=0.
M W
/V‘ N'
\ 9N ‘
”1 / "’" 1"" /I) A x)—  ' ‘
’ 7 7L lev‘CJcmﬂ '1“ 42 Jh(/’Uj2) 1' C 6. Solve the DE 1
7. Verify that yl (x) = E is a solution to the following DE. Then use the reduction of
order formula to ﬁnd a second linearly independent solution. $231” + 3xy' + y = 0. j/Vlﬂ} :y—r j,({)c] : ,— XP' 2'
6f”): '1 f3 x Lj,” +— siw,’ + 3 : i _ 3
”X ”Sc “LB/C: 6”»
/ jNoch
‘32 3 \JJ ix
v3); 7C Y”?
A g *\w~“
X x >4 X 8. Solve the DE 9. Solve the DE y" +4y'+ 3y = 0. ASSOSIM {lawn/w
ml 4‘ Lin/1+ 3 :O (MALE/X/Mw/ia M: ~ 51m: v
, my
6 3 ‘2 Q» <
X\(LJ7L) 10. Solve the DE 3/” +4y’ + 53/ = 0. 10 ...
View
Full Document
 Spring '09
 Math

Click to edit the document details