Winter Final Paper Differential-Equations-01-Solutions, guaranteed and verified 100% Pass

PRIME REVIEW ONLINE
MECHANICAL ENGINEERING REVIEW
MATHEMATICS &BASIC ENGINEERING SCIENCES
PRIME'S SUPPLEMENTARY ENHANCERS (DIFFERENTIAL EQUATION 01
DIFFERENTIAL EQUATION 01 x'y=4+Cy
PSE MODULE 8.1 (SOLUTION) Dividing both sides by y:
x' = 4y+C

1. What is the solution to the following differential equation y' + 5y = 0?
dr
A. y=5x +C C.y=CeS
B. y=CeS D. either A or B 2x-4yy'+0
xy +2y=0
Solution:
2y+ = 0
y'+5y =0 =dx -5y =-Sdx Ans. C
y
6. Which ofthe following is the differential equation ofy =Cicos 3x +Czsin
3x?
Iny=-5x+C
y=e* =e
A. y-9y C.9y-y= 0
B. y+9y=0 D. 9y +y=0
y=Ce

Ans. B Selikoni

2. The solution of the differential equation xdy - y dx represents which of
y=Ccos3x +Csin3x0
the following? y'=-3Csin3x +3C, cos 3x
A. straight line passing through
the origin y-9C,cos 3x 9C, sin3x3
B. parabola whose vertex is at the origin From
C. circle with center at the
origin - 9 (Ccos3x +C sin3x)
D. rectangular hyperbola
Subs. into y
Seluren:

xdy-ydr =0
d -9(y)
y+9y=0
Ans. B
-- Iny-nx=Ine 7. The differentialequation (y"-Sx(y°*= e + 1 is of degree
A C 2
y c r t h i s is straight line pussing through the origin B. 3 D. 4

Alernate Solution: Salilpn
xdy-ydr=0
(-5x(- e+
m mathisis straight hne passingthrough the onigin degree
dx
Ans. A Ans. B
3. The differential equation of all straight lines whose slope is m and whose 8. dQ/dt kQ then Qis equal to
A. Q=ce CQ=ce
y-intercept is b.
B. Q=ce D. Q=ce
A. y - y = 0
C.y+y0
B. y=0 Dy=0 Seliion:
Seltion:
y= mx+b dt
dQkdi
dt

dy = m
dx

lnQ=k+C
dy-0
dx
=0 Q=e where e C
Ans. D Q=Ce"
4. The coeficients of dx and dy of the equation xydx + ( + ydy = 0 are D
homogeneous functions of degree
C.3 9. The ditferential equation y" 5xy'H= e+ l
A 2
D. 6 is of order
B 4

Seluion:
C.2
B.4 D. no order
x*ydx +(x'+ y )dy=0
Sol.on:
Degi Legoe
-5x (Y= e+1
Ans. C Order 2

5. What is the differential equation of x'y = 4 + Cy. Ans. C
A. 2x + xy' = 0 C. 2y' + xy=0
B. 2y'+xy"=0 D. 3y' +4y" 0 10. Which of the following is an exact differenüal equation?
A. (2xy-3yxlx + (x3xdy = 0
Selutie B. (2xy-y dx - (x* + xy>xly =0
C. (2x +xydy + 2ydx =0
D. xdy- ydx = x2Inx dx

, PRIMEREVIEW ONLINE
MECHANICAL ENGINEERING REVIEW
MATHEMATICS &BASIC ENGINEERING SCIENCESs
PRIMES SUPPLEMENTARY ENHANCERS DIFFERENTIAL EQUATION 01

Selutom
Solelion
Perpenlicular :m,m, =-1
Check A.(2xy - 3ydx»(x-xdy =0 Check B(2xy- y)k x y d y

2x-3and 2x-3 oy
2x3y and -2x-y At x =1

Since exact M neN
y

Check C (2x4xydy 2ydx= 0 Check D. xdy - ydx = x-Ins dx
m2
Equating
M-2and-2-y
dy
(xInx+dx xdy0
M unexat
M and I k=7
y x dy

unexaet Ans. D
15. From the differential equation dy =x' dx. What is the equation of y
Ans A in terms ofx as the curve passes through ( 1, 1
x2-3y+ 3 0 x + 3 y +2 = 0

I1. Any function of y/x is homogeneous of degree B. x 3 y + 2 0 D. 2y+ x + 2 =0
A. C.T
B.2 D.3 Solation
Salelien:
dy=a'dx
x
1-1=0 Degree 0
Ans.A yx+C
12. A particle moves according to the following functions oftime: A(1.)
x(t 3sint and y(t) 4cost
What is the resulhant velocity at t ? C=2/3
A0 C.4 Subst.C 2/3 into y=
B. 3 D.9
3y+2=0
Ans. B
Seltion
16. The equation y= Cx is the general solution of
A.y2y Cyy/2x
Mode Radd B.y' 2xy D. y' x2y

Soletion
V,= 3units/sec
y Cx y=C
Ans.B

13. The integrating factor of the differential eguation ydx - xdy = 0 is:
2yy'y)=0
y2 C. x 2y+y-o
B. 1y2 D. I/x 2y' y/x
Seluhon 2x
ydx ady 0 Ans. C
M N
P(x)-
) - ) 112 17. Find the orthogonal trajectories of the given famiBy of curves x* + y*
x C
A.y kx C.y=kx
B.xy C D. y kxy
ON OM Sol.tio
x+yc
M

=e 2x+2yy=0 2yy 2x

Ans. B
The othogonal slope: m, -
14.Given: . What is dhe value of k such that y

is perpendicular to the curve y2 = 2x al (1, 1)?
tlhen:
dy dy xK
2 C.6

B. 3 D. 7
n|yl = n Ix|+Is
ycX
Aus A