Page 111 - Engineering Mathematics Workbook_Final

Differential Equations & Partial Differential Equations
( )
(a) e + sinh ( ) 1 (b) cosh 1 166. The particular integral of
( D − 4D + ) 4 y = x is
2
2
( )
(c) sinh 1 (d) cosh 1 +
( ) 1
1   3  
(a)  x + 2 2x +   
163. Suppose ( ) x = x cos2x is a 4  2 
y
p
particular integral of 1   x + 2 2x − 3  
y +  y = − 4sin2x, then the (b) 4   2    
11
constant  is 1  3 
(c)   x − 2 2x +    
(a) -4 (b) -2 4  2 

(c) 2 (d) 4 (d) 1   x − 2 2x − 3  
4   2    
164. The particular integral of the
differential equation 167. The particular integral of the
( D − 4D + ) 3 y = cos x is differential equation
2
( D − 4D + ) 4 y =  2x
2
x e is
cos x − 2sin x
(a) xe 2x x e
2 2x
10 (a) (b)
6 6
cos x + 2sin x
3 2x
3 2x
(b) x e x e
10 (c) (d)
24 6
2cos x − 4sin x
(c) 168. The particular integral of
5 ( D − 5D + ) 6 y = e 2x cos x is
2
2cos x + 4sin x 2x
(d) (a) − e sin
5 (cos x + ) x
2
165. The particular integral of e 2x
( D − ) 9 y = e + sin2x is (b) − 2 (cos x − sin ) x
3x
2
e 3x sin2x e 2x
(a) + (c) (cos x + sin ) x
6 13 2

e 3x 1 e 2x
(b) − sin2x (d) (cos x − sin ) x
6 32 2

e 3x 1 169. The particular integral of the
(c) − sin2x
6 13 differential equation
2
x
xe 3x 1 ( D + ) 9 y =  sin2x is
(d) − sin2x
6 13

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