Page 112 - Engineering Mathematics Workbook_Final

Differential Equations & Partial Differential Equations

sin2x 4 (b)
(a) x  + cos2x
5 25 y = c 1 + c cos (log x + sin (log x
))
) c
x ( 2 3
x sin2x 4
(b) − cos2x (c)
5 25
y = c + x c cos (log x + 3 sin (log x ))
) c
( 2
1
x 2 sin2x 4 (d)
(c) + cos2x
5 25 y = c x + x c cos (log x + 3 sin (log x ))
2
) c
( 2
1
(d) None
170. The particular integral of 173. The differential equation for which x
2
x
( D + 2 ) 4 y = x cos2x is , ln x and x are independent
solutions is
x 2 sin2x x 2 sin2x
3 111
2 11
1
(a) (b) (a) x y + x y − 3xy + 3y =
0
4 8
2 11
3 111
1
0
x 2 cos2x x 2 cos2x (b) x y − 2x y + 3xy − 6y =
(c) (d)
4 8
2 11
1
3 111
0
(c) x y − x y + 2xy − 2y =
171. The particular integral of
11
1
0
( D + 2 ) 9 y = sec3x is (d) y 111 − y + 2y − 3y =
x cos3x 174. Consider the differential equation
)
(a) sin3x + log (cos x x y − 3xy + 4y = then the two
2 11
1
0
3 9
linearly independent solutions of the
x cos3x differential equation are given by
)
(b) sin3x + log (cos3x
3 9
3
,
2
2
,
(a) x x (b) x x 2 / nx
x sin3x
)
(c) cos3x + log (sec3x x
3 3 (c) v (d) , x xe
x sin3x 175. The partial differential equation
)
(d) cos3x + log (cos3x 2 2 2
3 3  y  u  u
2 + 4 + 3 = 2 is

 x 2  x y  y 2
172. The general solution of the
differential equation (a) Elliptic (b) Hyperbolic
3
( x D + 2x D + ) 2 y = is
3
2
2
0
(c) Parabolic (d) None
x
+
(a) y c x= 1 + ( cosc 2 x c 3 sin ) x e

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