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BS (ME), 2™ Semester
Differential Equations
SESSIONAL TEST-I
Time Allowed: 1 hour 30 minutes Total Marks: 25 Date: May 5, 2011
Attempt the following questions.
1. Find the solution of the differential equation
® = 6x(y 16
2. Find a general solution of
(x? + je + 3xy = 6x
3. Solve the differential equation
(6xy —y Jae + (4y 43x? —3xy? dy =0
4, Suopose that 240 anda #1. Show that the substitution v = y'™ transforms the Bernoulli
equation a + P(x)y = O(x}y" into linear equation +(1-n)P(x)(x) = 0- role).
4 a
t ree gd
5. Solve by the method of undetermined coefficients
3
fy @ = 2x? +4Sinx
dx’ dx
& : Page 1/1
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Sobsstion et
recsimmal Text-T
Lacon a ont
Gorse i Digygrerdiol Ge :
LSM and Remasler.
0
f Bow be an
Selohiow te .
ay gx(a-))
dat
Separrokion ah yoriables apes
dy = 2 xAx
2a a
3 (9-1)
jrtegracingy
: dy = 2 fan
( 3 (3-3 3
\/3 2, { naa
+ (cS) ly =
sen .
2 (4-1) 1 Bye
hah
3
(ji)
%
j-1)*= Gc) .
qo = I* (x9 Anco
e+ c
ee
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| a
Spluborw Te Q, A
a =Q(r\y”
co + POY ey
Wek V= yo
|
ove
a =n a
ay ei av
a in8 on
. i Becomes
The apron diggerential caret
De __ Oe
_| yi + 9@).V) "-Q@-V
1-1 on
aR whos Dy
FR y (oa) P@V = (nO V"
yin ee O-n) 2 _ .
Dividing both SAM MY Y we e
a »)
Vv _n) OCR va) =b-r) &l
av x (i-n) 0 @) se Aaguineck
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- Lo dution ye Q.S &
e 2
at 5 AD 2 2h + 4Sinn
aye lth
lo find te character dibe Guation 35
y+7 =0
¥ (= D
eet =
yd) yrs
Om
feo
y= *)
Yao
2
: d= Q, + Cy Cag A-r Ca SinK
Te find df
”) Ab + 4a ot
WP, = a (aitvbaed) = Ave RECA
4 = SARE rUPIT Cc
4, = 6Anx 26
dy, =
~ &A BAN EURAEC =H”
> MASOA sA-2 >\
6A+CHO
6ke xc »|c=-4\
~A eso > (tad
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> = % (9 cesx + BSiv4) = A AGA +haSinr
d= Nass —a8ini| +B | Sinn + asx
= AC&xA- AxSina>+ RRina + RAGIN
;
We.
40, = pina — AGinn— AnCo8H > BCS BOE
* —RASinr
; _anSinns 2G — An Gan BASEN
the. =
ja Sinn — BSI OA
4p. = = —QAGEA —2R Sina — ACoA +
se | Qa Gor
fl = BA Cos BB Sinn Aa Sinn BAGS
Or
wes
* ra Gnr— Bain A GS a~ ~ hySivn
= 3 AC&A—TRSInA
+ bina + BaGesr = ASiw&
> -wb+8=4
AO Pera => G=-v
mA a pnaA=o =>fAz0
Ys 9% = — LASinA
Wonce veoh Sabuctton yi
y 4.) + OP, + PL
ye
G(x) = Cyr C2 GIA + CQ Sinn F a 4X ~2ASI HA
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