Page 99 - Engineering Mathematics Workbook_Final

Differential Equations & Partial Differential Equations

−
−
(a) K e ( 1+ ) 6 x + K e ( 1− ) 6 x 86. Consider the differential equation
( )
x +
0 with initial
( ) 27y x =
2
11
1
3y
1
y
y
0
−
−
(b) K e ( 1+ ) 8 x + K e ( 1− ) 8 x conditions ( ) 0 = and ( ) 0 = 2000 .
2
1
The value of y at x = 1 is
−
−
(c) K e ( 2+ ) 6 x + K e ( 2− ) 6 x ___________.
1 2
[GATE-2017-ME-SECTION-2]
−
−
(d) K e ( 2+ ) 8 x + K e ( 2− ) 8 x
1 2 87. The general solution of the
differential equation
[GATE-2017-EC-SECTION-2]
3
4
2
d y d y d y dy
84. Consider the following second-order 4 − 2 3 + 2 2 − 2 + y = 0
differential equation: dx dx dx dx
+
(a) y = (c − c 2 ) x e + c 3 cos x c 4 sin x
x
1
1
2
11
y − 4y + 3y = 2t − 3t
+
x
(b) y = (c + c 2 ) x e − c 3 cos x c 4 sin x
1
The particular solution of the
+
differential equation is (c) y = (c + c 2 ) x e + c 3 cos x c 4 sin x
x
1
−
− −
−
x
(a) 2 2t t − 2 (b) 2t t − 2 (d) y = (c + c 2 ) x e + c 3 cos x c 4 sin x
1
− −
2
2
(c) 2t − 3t (d) 2 2t − 3t [ESE-2017 (EE)]
[GATE-2017-CE-SECTION-2] 88. The solution of the differential
equation
85. The differential equation
2
d y + 16y = 0 for ( ) x with the d y − dy − 2y = 3e ,
2
2x
y
dx 2 dx 2 dx
dy
1
0
y
y
two boundary conditions = 1 where, ( ) 0 = and ( ) 0 = − 2 is
dx x= 0
dy (a) y e= − x − e + xe
2x
2x
and = − 1 has
dx x= 
2 (b) y e= x − e − 2x − xe
2x
(a) no solution
(c) y e= − x + e + xe
2x
2x
(b) exactly two solutions
(d) y e= x − e − 2x + xe
2x
(c) exactly one solution
(d) infinitely many solutions [ESE-2018 (EE)]
[GATE-2017-ME-SECTION-1]

97