Page 134 - Engineering Mathematics Workbook_Final

Differential Equations & Partial Differential Equations
     k    x    − k        x  2 y  2 y

(a) cos kt  C ( ) C e      + C e          (d) t  2 = c 2  x 2

2
1
   
309. The number of arbitrary constants in
     k    x    − k        x the general solution of one
(b) Ce  kt C e      + C e        
 1 2  dimensional wave equation is
   

310. Which of the following differential
(c) equations is parabolic?
     
kt   k   k  
+
Ce  C cos  x C sin −   x
   1      2           (a) one dimensional wave equation


(b) one dimensional heat equation
(d) (c) Laplace equation
    k   k   




+
C sin kt C cos  x C sin −   x (d) Poisson’s equation
   1      2        


 
311. The solution of the equation
 2 y  2 y
 u  u = 4 , representing the
306. The solution of 3 + 2 = 0, t  2  x 2
 x  y vibrations of a string of length 5
( ,0 =
x
−
u x ) 4e subject to the conditions,
 y
0,t =
5,t =
 2 u  2 u y ( ) 0; y ( ) 0; t  = 0
)
307. The equation + = f ( ,x y
 x 2  y 2 when t = 0 and
( ,0 =

is y x ) sin2 x −  2sin5 x is
(a) Elliptic (b) Parabolic  2 u  2 u
312. The solution of = with
(c) Hyperbolic (d) circular t  2  x 2
0,t =
1,t =
u x
u ( ) u ( ) 0; ( ,0 = and
) 0
308. The one dimensional wave equation
is  u ( ,0 =
x
) u (u is a constant) is
t  0 0
 2 u  2 u
(a) + = 0
 x 2  y 2 313. A tightly stretched string with fixed
end points x = 0 and x l = is initially
 2 u  2 u in a position given by
)
(b) + = f ( ,x y
 x 2  y 2   x  
y = y 0 sin 3  l    . If it is released
 u  2 u  
(c) = c 2
t   x 2

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