Page 124 - Engineering Mathematics Workbook_Final

Differential Equations & Partial Differential Equations

2 at x = 1, calculate the displacement 2 dy + 2xy = 2log x
1 242. If x dx x and y(1) = 0
at x = [GATE-1998]
2 then y(e) = 0

2 11
1
239. The solution to x y + xy − = 0 (a) e (b) 1
y
1
is (c) (d) 1
e e 2
−
=
3
(a) y C x + 1 2 C x
2
[GATE]
−
2
(b) y C= 1 + C x  u  u
2
243. The solution of = 4 ,
C  x  y
=
(c) y C x + 2 − 3y
1
) 8e
x u (0, y = is _________
4
+
=
u
) 8e
(d) y C x C x (a) ( , x y = − 12x− 3y
1
2
u
) 8e
[GATE-2015 (PI)] (b) ( , x y = − 3x− 12 y
240. The differential equation for which x, (c) ( , x y = − 3y− 4x
) 8e
u
2
x ln x and x are independent − 3x− 3y
) 8e
u
solutions is (d) ( , x y =
3 11
2 11
1
0
(a) x y + x y − 3xy + 3y = 244. The solution of p + q = 1 is
_____
1
(b) x y − 2x y + 3xy − 6y =
2 11
3 11
0
+
=
+
(a) z ax by c
3 11
1
(c) x y − x y + 2xy − 2y = ( ) 2
2 11
0
+
(b) z = ax + 1− a y c
1
11
0
(d) y 111 − y + 2y − 3y =
)
+
(c) z = ax + ( 1− a y c
[CSIR]
+
(d) z = ax − ay c
241. Consider the differential equation
p +
x y − 3xy + 4y = then the two 245. The solution of (1 q = ) qz is
2 11
1
0
linearly independent solutions of the ______
differential equations are given by
+
+
=
(a) az − 1 e x ay c
3
2
2
,
,
(a) x x (b) x x 2 ln x (b) z e= x ay c
+
+
x
(c) v (d) ,x xe
(c) z ax by c= + +
)
+
[CSIR] (d) z = ax by + f ( ,a b

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