Page 97 - Engineering Mathematics Workbook_Final

Differential Equations & Partial Differential Equations

71. Consider the following second order Given ( ) 0 = 20 and ( ) 1 = 10 / e,
x
x
linear differential equation
x
2
d y = − 12x + 24x − 20. The where e = 2.718, the value of ( ) 2 is
2
dx 2 ___________.
boundary condition are at x = 0, [GATE-2015-EC-SET-3]
y = 5 and at x = 2, y = 21

The value of y at x = 1 is _________. 75. A solution of the ordinary differential
2
d y dy
[GATE-2015-CE-SET-2] equation + 5 + 6y = is
0
dt 2 dt
2
d y
72. Find the solution of = y which such that ( ) 0y = 2 and
dx 2
−
passes through origin and point y ( ) 1 = − 1 3e . The value of dy ( ) 0
 3  e 3 dt
 ln2, 
    is _________.
 4 
1 − [GATE-2015-EE-SET-1]
x
(a) y = e − x e
2
2
1
11
y
76. The solution to x y + xy − = 0 is
1
(b) y = (e + x e − x )
=
2 (a) y C x + 2 C x
−
3
1 2
1
(c) y = (e − x e − x ) (b) y C + C x
=
−
2
2 1 2
1
−
x
(d) y = e + x e (c) y C x + C 2
=
2 1 x
[GATE-2015-ME-SET-1]
+
4
=
(d) y C x C x
73. The solution of the differential 1 2
2
d y dy
equation + 2 + y = 0 with [GATE-2015-EC (PI)]
dt 2 dt
1
y
y
y ( ) 0 = y 1 ( ) 0 = 1 is 77. A function ( ) t , such that ( ) 0 =
−
1
y
)
)
−
t
t −
+
(a) (2 t e (b) (1 2t e and ( ) 1 = 3e , is a solution of the
differential equation
t
2
(c) (2 t e+ ) t − (d) (1 2t e− ) d y + 2 dy + y = 0. Then ( ) 2y is
dt 2 dt
[GATE-2015-EC-SET-1]
−
1
(a) 5e (b) 5e − 2
74. Consider the differential equation
−
−
2
1
2
d x ( ) t dx ( ) t (c) 7e (d) 7e
+ 3 + 2x ( ) 0t =
dt 2 dt [GATE-2016-EE-SET-1]

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