Page 135 - Engineering Mathematics Workbook_Final

Differential Equations & Partial Differential Equations

from rest from this position then the
y
, x
displacement ( ) t is.

 u  2 u
314. The solution of = c 2 ,
t   x 2


0 x  , t  0 under the boundary
u 
0,t =
) 0
u
conditions ( ) 0, ( ,t =
and ( ,0 =
u x
) sin x . Where


0 x  is
, x
u
315. What is the temperature ( ) t in a
laterally insulated copper bar 80 cm
long if the initial temperature is
 x  0
100sin       C and the ends are
 80 
0
kept at 0 C ?

 2 u  2 u
316. The solution of + = 0 with
 x 2  y 2
the conditions
)
u (0, y = y ( , l y = ( ,0 = and
) u x
) 0

n x
u ( , x a = is.
) sin
l
 2 u  2 u
317. The solution of + = 0 with
 x 2  y 2

) 0
u
the boundary conditions (0, y = ,
=
) 0 u
u ( , l y = , ( , x  ) 0 and
u ( ,0x ) u= 0 is (where 0 x ls  ).

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