Page 108 - Engineering Mathematics Workbook_Final

Differential Equations & Partial Differential Equations

3 3 (a) ( x − x 2 y 2 ) c
=
e
(a)  , = = 1 (b)  1, = =
2 2
e
(b) ( x + x 2 y 2 ) c=
2 2
(c)  , = = 1 (d)  1, = =
3 3
=
−
(c) ( x + x 2 y 2 ) c
e
144. The differential equation
−
=
e
( 27x + ky cos ) x dx + (2sin x − 27y 3 ) dy = 0 (d) ( x − x 2 y 2 ) c
2
is exact for k =
148. If the integrating factor of
(a) 2 (b) 3 7 2 3
( x y + 3y ) dx + (3x y − ) x dy =
0
(c) 4 (d) 5  
is x y then
145. The integrating factor of (a)  7,  = − = 1
)
(Cos sin 2x dx + (cos y − cos 2 ) x dy = 0
2
y
is (b)  1,  = = − 7

(a) sec y + 2 sec y  tan y (c)   = = 0

(b) tan y + 2 sec y  tan y (d)   = = 1

1 149. The solution of
(c) 2 2
0
sec y + 2 sec y  tan y ( y − xy ) dx − ( x + x ) y dy = is

1  x  x
(d) (a) ln     − = c
tan y + 2 sec y  tan y   y   y

146. Consider the differential equation  x  x

dy = (3x + 2x )e y x + 1, if ( ) 1y = 1 (b) ln       + = c
−
2
dx  y  y
y
then ( ) 0 =  x 
=
(c) ln       + xy c
−
3
(a) log (b) 0  y 
e
 x 
3
=
(c) 1 (d) log (d) ln       − xy c
e
 y 
147. The solution of the differential
equation 150. The orthogonal trajectory of the
( x + y + 2x ) dx + 2ydy = is family of circles x + 2 y = 2 2cx is
2
2
0
described by the differential equation

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