Page 93 - Engineering Mathematics Workbook_Final

Differential Equations & Partial Differential Equations

1 1
x
(a) c e − 2x + c e − 3x e (c) e x /2 + 2cos4x + 5sin4x
1
2
4 5
1 (d) 2cos4x + 5sin4x
x
(b) c e + 2x c e + 3x e
1
2
4
[JAM GP 2005]
1
x
(c) c e + 2x c e − 3x − e 52. Consider the differential equation
1
2
4
y + 6y + 25y = with initial
1
11
0
1
x
(d) c e − 2x + c e + 3x e condition ( ) 0 = . Then, the
y
0
1 2
4
general solution of the initial value
[JAM MA 2008] problem is
y
50. The solution ( ) x of the differential − 3x
+
(a) e ( cos4A x B sin4x )
2
d y dy
0
equation + 4 + 4y = − 3x
dx 2 dx (b) Be sin4x
4
y
satisfying the conditions ( ) 0 = , − 4x
(c) Ae sin3x
dy ( ) 0 = is
8
+
A
dx (d) e − 4x ( cos3x B sin3x )
2x
(a) 4e [JAM GP 2006]
(b) (16x + ) 4 e − 2x 53. The differential equation
2
d y + y = 0 satisfying ( ) 0y = 1,
(c) 4e − 2x + 16x dx 2
y  =
( ) 0 has
2x
(d) 4e − 2x + 16xe
(a) a unique solution
[JAM MA 2011]
(b) a singly infinite family of
51. The particular integral of the
following differential equation solutions
(c) no solution
y + 11 2y + 1 5y
(d) a doubly infinite family of
5
= e x / 2 x + 18cos4x − 71sin 4x is solutions
4 [JAM GP 2008]
54. The particular integral of the
5
(a) e x /2 + 5cos4x differential equation
4
y + y + 3y = 5cos (2x + ) 3 is
11
1
(b) 5cos4x + 2sin4x

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