8.分离变量 tt 00(x,)x0=0v(x,1)=0 l=0=(x)u4=0=v(x) 波腹 l(x,)=X(x)T(1) 0.5 波节 7.5 T=0:X+X=0 X(0)=0 X()=08. 分离变量 0 2 utt − a uxx = ( ) 0 u x t= = ( ). 0 u x t t= = u(x,t) x=0 = 0 u(x,t) x=l = 0 波腹 波节 2.5 5 7.5 10 12.5 15 -1 -0.5 0.5 1 u(x,t) = X (x)T(t) '' 0; 2 T +a T = X ''+X = 0; X (0) = 0 X (l) = 0