Page 125 - Engineering Mathematics Workbook_Final

Differential Equations & Partial Differential Equations

246. The solution of p + q = + is 249. The partial differential equation that
2
2
y
x
can be formed from z = ax + by + ab
____
has the form
+
=
+
(a) z ax by c   z  z   
  with p = and q =  
2 3/ 2 2 3/ 2   x  y 
+
−
(b) z = (a x ) + ( y a ) + b
3 3
(a) z = px + qy
3 2/3 3 2/3
−
(c) z = (a + ) x + ( y a ) + b (b) z = px + pq
2 2
−
(d) z = (a + ) x 1/2 + ( y a ) 1/2 + b (c) z = px + qy + pq
(d) z = py + pq
247. The general integral of the partial [GATE-2010-CE]
differential equation
y p xyq = ( x z − 2y ) is 250. The complete integral of
2
−
(
)
2
3
2
−
(z − px qy ) = pq + 1 p + q is
)
2

2
(a) ( x + y 2 , y − yz = 0
(
)
+
2
2
2

(b) ( x − y 2 , y + yz = 0 (a) z = ax by + 3 pq + 2 p + q ) 2
(
2
+

) 0
,
© ( xy yz = (b) z = ax by + 3 ab + 2 a + b ) 2
−

(d) (x + y ,ln x z = 2
) 0
2
+
(c) z = ax by + 3 ab + 3 ( 2 a + ) b
+
+
=
[ESE 2018 (EE)] (d) z ax by c
248. The solution at x = 1, t = 1 of the [ESE 2017 (COMMON PAPER)]
partial differential equation
 2 u = 25  2 u subject to initial 251. The solution of the following partial
2
2
 x 2 t  2 differential equation  u = 9  u is
2
2
conditions of u(0) = 3x and  x  y
 u 3 (a) sin (3x − ) y (b) 3x + y
2
2
t  ( ) 0 = is ______
2
(a) 1 (b) 2 (c) sin (3x − 3y ) (d) ( 3y − x 2 )
© 4 (d) 6 [ESE 2017 (COMMON PAPER)]
[GATE-2018 (CE-MORNING SESSION)]

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