Page 107 - Engineering Mathematics Workbook_Final

Differential Equations & Partial Differential Equations

+
137. If y − 1 x  0 then the solution of the (c) cos y = (x c )sin x
differential equation
+
(d) sec y = (x c )cos x
1
y 1 ( y + ) y = ( x x + ) y with
2
y ( ) 0 = is 141. The general solution of the
differential equation

x
+
−
(a) 1 x e− + − x (b) 1 x e dy + x sin2y = x 3 cos y is
2
dx
(c) 1 x e+ + − x (d) 1 x e+ + x
1 − 2
2
c e
dy 2log x (a) Tan y = ( x − ) 1 +  x
138. If x 2 + 2xy = and 2
dx x
y
0
y ( ) 1 = then ( ) e = (b) Tan y = 1 ( x − ) 2 +  − x 2
2
c e
2
(a) e (b) 1
2
c e
(c) Tan y = ( x − ) 1 +  − x 2
1 1
(c) (d)
e e 2 1 2
2
(d) Cot y = ( x − ) 1 +  x
c e
dy 2
139. If + 2 Tan x = y Sin x and
dx 142. The general solution of
   dx
y       = 0 then the maximum value ( x y + 3 2 xy ) = 1 is
 3  dy
of ‘y’ is − 1
2
2 c e
(a) = x − +  − x 2 /2
1 1 y
(a) (b)
4 8

+
2
(b) 1 = x + 2 c e − x 2 /2
1 y
(c) 2 (d)
2
1 2 x 2 /2
2 c e
140. The general solution of the (c) y = x + + 
differential equation
dy + Tan x  Tan y = Cos x  Sec y (d) 1 = x + 1 c e − x 2 /2

2
+
dx y
is
143. The differential equation
(a) 2sin y = (x c+ − sincos x )sec x ( xy 3 + y cos ) x dx +

(b) sin y = (x c+ )cos x ( x y + 2 2  sin ) x dy = 0 is exact for

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