Page 92 - Engineering Mathematics Workbook_Final

Differential Equations & Partial Differential Equations

1
45. The solution of the differential (a) ( xe + 4x − 4x −
2
d y 8 xe ) 1
x
equation − y = e satisfying
dx 2
1
dy 3 (b) ( xe − 4x − 4x +
0
y ( ) 0 = and ( ) 0 = is xe ) 1
dx 2 8
x 1   4x − 4x 1  
x
y x =
(a) ( ) sinh x + e (c)  e − xe +   
2 4  2 
x  
x
(b) ( ) x = y x cosh x + e (d) 1  xe − 4x e − 4x + 1 
2 4   2    
x
y x =
x
(c) ( ) sinh x − e [JAM CA 2011]
2
48. A general solution of the differential
x
y x =
x
(d) ( ) 2 cosh x − x e d y d y
3
2
2 equation − 3 + 4y = is
0
dx 3 dx 2
[JAM CA 2010]
2x
x
2x
(a) y = c e + c e + c xe
46. The solution of the differential 1 2 3
3
d y dy −
2x
x
2x
equation − 9 = cos x is (b) y = c e + c e + c xe
dx 3 dx 1 2 3
−
x
2x
−
x
1 (c) y = c e + c xe + c e
1
2
3
(a) ( ) x = C e + C e − 3x + C + sin x
3x
y
3
2
1
10
−
4x
x
x
(d) y = c e + c e + c e
1 1 2 3
3x
y
(b) ( ) x = C e + C e − 3x + C − sin x
3
1
2
10 [JAM CA 2011]

y
y
49. Let ( ) x and ( ) x be twice
1 1 2
3x
y
(c) ( ) x = C e + C e − 3x + C + cos x
3
1
2
10 differentiable functions on a interval I
satisfying the differential equations
1
y
(d) ( ) x = C e + C e − 3x + C − cos x dy
3x
x
1
3
2
10 1 − y − y = e and
dx 1 2
[JAM CA 2010] dy dy
y
0
2 1 + 2 − 6y = . Then ( ) x
47. A particular integral of the dx dx 1 1
differential equation is
2
d y − 16y = 4sinh 2x is
2
dx 2

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