Page 105 - Engineering Mathematics Workbook_Final

Differential Equations & Partial Differential Equations

dy 4 + y 2 log3 log2
2
y
125. Consider = , if ( ) 1 = (a) 2 (b) 2
+
dx 1 x 2 log2 log3
y
then ( ) 2 = log3 log2
(c) (d)
(a) 0 (b) 5 log2 log3

(c) 14 (d) 21 129. The rate at which a body cools is
proportional to the difference
dy x (2log x + ) 1 between the temperature of the body
126. The solution of =
dx sin y + y cos y and that of the surrounding air. If a
0
is body in air at 25 C cools from
0
0
100 C to 75 C in one minute then
+
(a) sin y = y x 2 log x c
the temperature at the end of three
− +
y
(b) cos y = x 2 log x x c minutes is
0
0
(a) 47.22 C (b) 42.22 C
−
2
c
y
(c) sin y = x 2 log x x +
0
0
(c) 37.22 C (d) 39.22 C
− +
y
(d) sin y = x logx x c
130. A radium decomposes at a rate
dy proportional to the amount of radium
−
2 −
y
127. The solution of = e x y + x e is
dx present at that time. If 5% grams of
original amount disappears after 50
x 3 years then the amount disappears
−
x
y
(a) e = e + + c
3 after 50 years then the amount will be
remain after 1000 years is
x 3
−
x
(b) e − y = e + + c
3 (a) 95.95% of the original amount
(b) 95% of the original amount
x 3
x
y
(c) e = e + + c
3 (c) 90% of the original amount
x 3 (d) 90.25% of the original amount
−
x
(d) e − y = e + + c
3 dy 2
y
131. The solution of = (4x + + ) 1 is
128. The rate of which bacteria multiply is dx
proportional to the instantaneous 1  4x + 4y + 1 
number present, if the original (a) tan − 1       = c
number doubles in 2 hours then it will 2  2 
be triple in

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