Page 86 - Engineering Mathematics Workbook_Final

Differential Equations & Partial Differential Equations

+
(d) e / x y = x c (b) x 2 ( 2x e − y 2 ) = c
+
7. The differential equation 2
+
2ydx − (3y − 2x )dy = (c) x ( 2x e − y ) = c
0

(a) exact and homogeneous but not (d) x ( 2x e − y 2 ) = c
−
linear
[JAM CA 2006]
(b) homogeneous and linear but not

exact 10. The solution of the initial value
problem xy − 1 y = 0 with
(c) exact and linear but not 1
y
homogeneous xy − y = 0 ( ) 1 = 1 is

x
y
(d) exact, homogeneous and linear (a) ( ) x =
[JAM CA 2006] 1
y
(b) ( ) x =
8. The general solution of the x
y x =
differential equation (c) ( ) 2x − 1
(x + − ) 3 dx − (2x + 2y + ) 1 dy =
0
y
is (d) ( ) x = 1 [JAM CA 2007]
y
2x − 1
k
(a) ln 3x + 3y − 2 + 3x + 6y =
11. The solution of the differential
equation
k
(b) ln 3x + 3y − 2 − 3x − 6y =   x sin y − y cos y   dx x cos dy = 0
y
+
k
(c) 7ln 3x + 3y − 2 + 3x + 6y =   x x     x
y
0
with initial condition ( ) 0 = is
k
(d) 7ln 3x + 3y − 2 − 3x + 6y = y

x
(a) sin = 1 (b) y =  n x
[JAM CA 2006] x
9. The general solution of the y
differential equation (c) y = x sin x (d) x = y
( 6x − e − y 2 ) dx + 2xye − y 2 dy = 0 is
2
[JAM CA 2008]

12. The differential equation
2
−
(a) x 2 ( 2x e − y 2 ) = c (2x + by 2 ) dx cxydy+ = 0 is made
exact by multiplying the integrating

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