A.分离变量 l(x,y,t)=1()v(x 带入泛定方程+xv=07"+xa27=0 边界条件为 =0 0 再分离变量v(x,y)=X(x)(y) Xy+xr+hXY=0 X'Y+2v=-XY"y+/'v Yr" XY XY X"+(x2-12)X=0 X(O)=X()=0 y"+2Y=0 P(0)=(O)=0A. 分离变量 u(x, y,t) = T(t)v(x, y) 0 2 带入泛定方程 v +  v = '' 0 2 2 T + a T = 边界条件为： v x=0 = v y=0 = v x=l = v y=l = 0 再分离变量 v(x, y) = X (x)Y( y) '' '' 0 2 X Y + XY + XY = '' ( ) 0 2 2 X +  −  X = '' '' 2 X Y +  v = −XY 2 2 '' ''   = − = + XY XY XY X Y v '' 0 2 Y + Y = X (0) = X (l) = 0 Y(0) = Y(l) = 0