Page 98 - Engineering Mathematics Workbook_Final

Differential Equations & Partial Differential Equations

78. If y = f ( ) t satisfies the boundary (a)
 
+
+

value problem y + 11 9y = 0,   c + c x c 3 sin 3x c 4 cos 3x

2
1

)
y  ) 2 , then ( / 4 is and 3x −    4 12x + 2 c
( / 2 =
y 


_______________.

[GATE-2016] (b) c X +    2 c 3 sin 3x + c 4 cos 3x



79. The particular solution of the initial and 5x −    4 12x + 2 c


value problem given below is

+

2
d y dy (c) c +    1 c 3 sin 3x c 4 cos 3x

0
+ 12 + 36y = with

dx 2 dx and 3x −   4 12x + 2 c

dy  
y ( ) 0 = 3 and = − 36
dx x= 0 (d)
 c + c x c sin 3x c 
+
+

)

−
(a) (3 18x e − 6x   1 2 3 4 cos 3x

and 5x −    4 12x + 2 c


)
+
(b) (3 25x e − 6x
)
+
(c) (3 20x e − 6x [GATE-2016-CE-SET-1]
82. What is the solution for the second
)
−
(d) (3 12x e − 6x [GATE-2016] order differential equation
2
d y
80. Let y(x) be the solution of the dx 2 + y = 0, with the initial
differential equation dy
2
d y − 4 dy + = conditions y x= 0 = 5 and dx = 10 ?
4 0 with initial
dx 2 dx x= 0
+
dy (a) y = 5 0sin x
0
y
conditions ( ) 0 = and = 1.
dx x= 0
−
Then the value of y(1) is _______. (b) y = 5cos 5sin x
[GATE-2016-EE-SET-2] (c) y = 5cosx + 10x
81. The respective expressions for (d) y = 5cosx + 10sin x
complimentary function and
particular integral part of the solution [GATE-2016 (CH)]
of the differential equation
2
4
d y + 3 d y = 108x are 83. The general solution of the
2
dx 4 dx 2 differential equation
2
d y + 2 dy − 5y = in terms of
0
dx 2 dx
arbitrary constant K and K is
1
2

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