Page 116 - Engineering Mathematics Workbook_Final

Differential Equations & Partial Differential Equations
  dy  2  SOULUTION OF DIFFERENTIAL
2 
2
(a) r  1+        = x EQUATIONS
 dx   
   
197. A solution of the first order
   2 differential equation

2 
(b) y  1+  dy   = r
2
  dx       sin (x y )
+
)
+
x
    y 'cos (x y + = e − cos (x y )
+
x
  dy  2  is
2 
2
(c) x  1+        = r
 dx    ( x
    (a) sin x + ) y − e = constant
 2 x
2   dy   (b) e tan (x + y = ) constant
(d) y  1−        = r
2
  dx    
  x x
(
x
(c) cos x + ) y − e + e = constant
195. A spherical naphthalene ball exposed
(
x
x
to the atmosphere loses volume at a (d) sin x + ) y − e + e = constant
x
rate proportional to its instantaneous
surface area due to evaporation. If the [GATE]
initial diameter of the ball is 2 cm and
the diameter reduces to 1 cm after 3 198. Consider the following differential
months, the ball completely equation :
evaporates in
y y
+
(a) 6 months (b) 9 months ( x ydx xdy )cos x = ( y xdy − ydx )sin
x
(c) 12 months (d) infinite time Which of the following is the solution
[GATE-2006] of the above equation (c is an
arbitrary constant?
0
196. A body originally at 60 C cools x y x y
0
down to 40 C in 15 min when kept (a) cos x = c (b) sin x = c
y
y
0
in air at a temperature of 25 C .
What will be the temperature of the y y
body at the end of 30 min? (c) xy cos x = c (d) xy sin x = c

0
0
(a) 35.2 C (b) 31.5 C [GATE-2015-CE-SET-II]
0
0
(c) 28.7 C (d) 15 C 199. The solution of the differential
equation
[GATE-2007-CE]
( x + y + 2x dx + 2y dy = is
)
2
2
0

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