Page 88 - Engineering Mathematics Workbook_Final

Differential Equations & Partial Differential Equations

(b) 2x + 3 6xy + 3y = 2 c 23. One of the integrating factors of the
differential equation
2
2
2
c
(c) 2x + 2xy + y = ( y − 3xy ) dx + ( x − xy ) dy = 0 is
2
2
c
(d) x + 2xy + y = 1 1
(a) 2 2 ) (b) 2
x
[JAM CA 2011] ( x y ( ) y
20. The general solution of the 1 1
2
d y   dy   2 (c) ( ) 2 (d) ( )
xy
xy
differential equation =    
dx 2  dx 
is [JAM MA 2007]
=
y
(a) x c e − y + c e 24. Consider the differential equation
2
1
( ) dy =
2cos y 2 − sin y 2 0
( ) dx xy
=
(b) x c e + 1 y c (a) e is an integrating factor
x
2
=
−
(c) x c e − y + c (b) e is an integrating factor
x
2
1
=
(d) x c e + 1 y c y [JAM CA 2011] (c) 3x is an integrating factor
2
3
21. An integrating factor of (d) x is an integrating factor
dy
x + (3x + ) 1 y = xe − 2x is [JAM MA 2009]
dx
25. Consider the differential equation
x
3x
(a) xe (b) 3xe dy = ay by , where , a b  and
−
2
0
dx
3 x
x
(c) xe (d) x e y ( ) 0 = y . As x → +, the solution
0
[JAM MA 2005] y ( ) x tends to
22. If k is a constant such that (a) 0 (b) a/b
(x− ) 1 2
+
xy k = e 2 satisfies the (c) b/a (d) y
0
differential equation
dy [JAM MA 2010]
2
x
x = ( x − − ) 1 y + (x − ) 1 , then
dx 26. Consider the differential equation
k is equal to (x + + ) 1 dx + (2x + 2y + ) 1 dy = .
0
y
(a) 1 (b) 0 Which of the following statements is
true?
(c) -1 (d) -2
(a) The differential equation is linear
[JAM MA 2007]
(b) The differential equation is exact

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