Page 131 - Engineering Mathematics Workbook_Final

Differential Equations & Partial Differential Equations

[GATE – 2001 (ME)]  u  u  2 u
+ u = 2 is a
280. The partial differential equation t   x  x
 2  +  2  +   +   = 0 has (a) linear equation of order 2

 x 2  y 2  x  y
(b) non-linear equation of order 1

(a) degree 1 and order 2
(c) linear equation of order 1
(b) degree 1 and order 1
(d) non-linear equation of order 2

(c) degree 1 and order 1
[GATE – 2013 - ME]
(d) degree 2 and order 2
284. The type of partial differential
[GATE – 2007 (ME)] equation
 2 P  2 P  2 P  P  P
281. The partial differential equation that 2 + 2 + 3 + 2 − = 0
+
+
=
can be formed from z ax by ab  x  y  xdy  x  y
is
has the form
  (a) elliptic (b) parabolic
 z  z  
  with p = and q =  
  x  y  (c) hyperbolic (d) none of these
+
(a) z = px qy [GATE – 2016 – CE – SET-1]

(b) z = px + pq 285. The solution of the partial differential
 u  2 u
+
(c) z = px qy + pq equation t  =   x 2 is of the form

=
(d) z qy + pq  ( k /  ) x − ( k /  ) x
kt 
(a) cosC ( ) C e + C e   

1
2

[GATE – 2010 - CE]
282. The type of the partial differential (b) Ce  kt  ( k / ) x − ( k / ) x 
f   2 f   C e + C e  
1
2
equation = is
t   x 2
(c)
(a) parabolic (b) elliptic Ce  kt    C 1 cos ( / k  ) x C 2 sin − ( / k  ) x   
+
C
( )[C
(c) hyperbolic (d) nonlinear (d) sin kt 1 cos ( / k  ) x +
[GATE – 2013 (IN)] ( )
C 2 sin − / k  ] x
283. The partial differential equation
[GATE – 2016 – CE – SET-1]

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