Page 104 - Engineering Mathematics Workbook_Final

Differential Equations & Partial Differential Equations

118. A solution of the differential equation (a) 1, 2 (b) 2, 8
dy = y + 1 is _________ (c) 3, 8 (d) 4, 8

dx
122. The degree of the differential
(a) y = e − x 1 (b) y = e + x 1   2  2 1/4 3

equation y +   x   d y     = d y
2 
(c) y = e + x x (d) y = e x− 1     dx    dx 3
 
[IISC 2002] is

119. The differential equation (a) 2 (b) 3
2
d y + 4 dy + 4y = has solution (c) 4 (d) 1
0
dx 2 dx
_________ 123. The differential equation of the
family of circles of radius ‘r’ and
+
A
(a) cos2x B sin2x whose centre lies on ‘x’ axis
(b) Ae − 2x + Bxe − 2x 2    dy  2 
2
(a) r   1+   dx         = x
2x
2x
(c) Ae + Bxe     dy   2  
2
2x
(d) Ae − 2x + Be [IISC 2002] (b) y  2   1+   dx         = r
   
120. The solution of first order ODE (c) x  2   1+   dy   2   = 2
1
xy = xy + + + 1 is ________     dx         r
y
x
=
(a) y cx e − ( x ) 1 (d) y  2   1 −   dy   2   = r
2
  dx      
   
(b) y = cxe − x 1 124. The differential equation of the
family of curves of the form

+
(c) y = ce − x x y = Ax Bx is
2
(d) y ce= x − x − 1 [IISC 2005] (a) x y − 2xy + 2y =
1
2 11
0
121. The order and degree of the (b) x y + 2xy + 2y =
2 11
1
0
differential equation
  3  2 4/3 (c) 2x y − xy + 0
2 11
1
  d y   d y 2y =
2
 1 +   3     = 2 are
2 11
  dx    dx (d) x y − 2xy − 2y =
1
0

102