上游充通大 SHANGHAI JIAO TONG UNIVERSITY 入>0时，X"+九X=0→ X=Asin几x+Bcos√2x, X(0)=B=0, X'(I)+hX()=A(V元cos√l+hsin√)=0 三tanAl=-√元/h. →tanz=az,其中=k2,z=kl=Vl,a=-1/(hl) 有根zn∈(n-1/2)m,(n+1/2)π)，n=1,2, →同有值-（号=12L →固有函数X,()=A,sinx T'+a2九nT=0→ -a T(t)=Ce--Ce 12 (n=1,2,L→0, 0 sin cos , X X X A xB x λ λ λ λ > + =⇒ ′′ = + 时 (0) 0, ( ) ( ) ( cos sin ) 0 tan / . X B X l hX l A l h l l h λλ λ λ λ = = ′ += + = ⇒ =− 2 , 1,2, n n z l λ n   =    ⇒ =  固有值 L ( ) sin n n n z Xx A x l ⇒固有函数 = 2 tan , , , 1/ ( ). (( 1/ 2) ,( 1/ 2) ), 1, 2,... n z az k z kl l a hl zn n n λ λ π π ⇒ = = = = =− ∈− + = 其中 有根 2 TaT ′ + =⇒ λn 0 2 2 2 2 ( ) , ( 1,2, ) n n a z t a t nn n l T t Ce Ce n λ − − = = = L