Page 101 - Engineering Mathematics Workbook_Final

Differential Equations & Partial Differential Equations

98. The differential equation representing (a) 4 (b) 3
the family of circles touching y axis
at the origin is _______ (c) 2 (d) 1

(a) Linear differential equation of [IISC 2008]
first order
102. Consider the differential equation
(b) Linear differential equation of 2 2
( ) dy =
( ) dx xy
second order 2cos y − sin y 0.
Then ______
(c) Nonlinear differential equation of
first order
x
(a) e is an integrating factor

(d) Nonlinear differential equation
of second order (b) 3x is an integrating factor
−
x
[JAM 2006] (c) e is an integrating factor
99. If k is a constant such that + = (d) x is an integrating factor
3
( −1) 2
2 satisfies the differential [JAM 2009]
equation
dy 103. Consider the differential equation
2
x
x
x = ( x − − ) 1 y + − 1, then k
dx dy = ay by , where a, b > 0 and
−
2
is equal to ________ dx
y ( ) 0 = y as x →  , the solution y(x)
(a) 1 (b) 0 0
tends to _________
−
−
(c) 1 (d) 2
a
[JAM 2007] (a) 0 (b)
b
100. One of the integrating factors of the (c) b (d) y
differential equation a 0

( y − 3xy ) dx + ( x − xy ) dy = 0 is [JAM 2010]
2
2
_____ 104. The solution of
2
d y dy
0 y
4
1 1 dx 2 + 4 dx + 4y = , ( ) 0 = ,
(a) (b)
2
2
x y 2 x y y 1 ( ) 0 = is __________
8
1 1 2x
(c) (d) (a) 4e
xy 2 xy
(b) (16x + ) 4 e − 2x
[JAM 2007]
(c) 4e − 2x + 16x
101. The number of independent solutions
2x
of the differential equation 1 − (d) 4e − 2x + 16xe [JAM 2011]
2 11 + = 0 is _______

99