Page 133 - Engineering Mathematics Workbook_Final

Differential Equations & Partial Differential Equations

292. The general integral of the partial 295. If ‘a’ and ‘b’ are arbitrary constants
differential equation then the partial differential equation
2
−
y p xyq = ( x z − 2y ) is corresponding to the equation
+
z = ax by a + b is _________
+
2
2

2
2
(a) ( x + y 2 , y − yz =
) 0
296. If ‘a’ and ‘b’ are arbitrary constants
2
(b) ( x 2 − y 2 , y + yz ) 0= then the partial differential equation
corresponding to the equation

,
) 0
(c) ( xy yz = z = xy + y ( x − a 2 ) + b is
2
2

−
) 0
(d) (x + y ,ln x z =
297. Form a partial differential equation
[ESE – 2018 (EE)] by eliminating the arbitrary function
from the relation
293. The solution at x = 1, t = 1 of the 2
partial differential equation z = y + 2 f (1/ x + log ) y .
 2 u = 25  2 u
 x 2 t  2 subject to initial 298. Form a partial differential equation
conditions of ( ) 0 = 3x and by eliminating the arbitrary function
u
from the relation
 u ( ) 0 = is _____________. ( f x + y 2 ,z − xy =
2
) 0 .
3
t 
−
(a) 1 (b) 2 299. The solution of p q = log (x + ) y .
(c) 4 (d) 6 300. The solution of
)
−
y x
[GATE – 2018 – CE – MORNING (z − ) y p + (x z q = −
SESSION]
301. The solution of q = 3p is
2
294. Consider a function it which depends
on position x and time t. The partial 302. The solution of q = 2 2 2 − 2 )
differential equation z p (1 p is

 u  2 u 303. The solution of p + q = + y is
2
x
2
= is known as the
t   x 2
304. The solution of
)(
(a) Wave equation ( p q z − px qy =
−
−
) 1 is
(b) Heat equation
 u  2 u
(c) Laplace’s equation 305. The solution of the PDE = 
t   x 2
(d) Elasticity equation is of the form

[GATE – 2018 – ME – AFTERNOON
SESSION]

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