8 at 22= Bu u(x, t)=X(x)T( XT-a2'X"T=BYT XT XT axt rT-B/a T-Br a'x T X T"+(a2-B)T=0 X+X"=0 又 X(0)=0和X()=0 n X(x)=C,sin n丌 n=1,2,3 T(t=Cexp[(B-2)t B 1=a/B8. u x u a t u =    −   2 2 2 u(x,t) = X (x)T(t) XT'−a X''T = XT 2 2 2 / ' '' a XT X T a XT XT − =    = = − − X a X T T' T '' 2 ' ( ) 0 2 T + a −  T = X + X'' = 0 又 X (0) = 0 和 X (l) = 0. l n x X x C  ( ) = 2 sin 2 2 2 l n   = n =1,2,3 ( ) exp[( ) ]; 2 2 2 2 t l n a T t C  =  − 2 2 ( ) a l n c   = n =1 l c = a / 