解u=XY a,(x)x"Y+b(xr +a,(xxy+b,(Xr=o a,(xx +2(x)y b,(y)r b,(r' 0 Y Y a()x"+2(x)X=(yy+2(y)y=-2 Y a1(x)X"+a2(x)X+X=0 6, r+b, rnr=0解 u = XY a1 (x)X''Y +b1 (y)XY''+a2 (x)X'Y +b2 (y)XY' = 0 0 ( ) '' ( ) ' ( ) '' ( ) ' 1 2 1 2 + + + = Y b y Y Y b y Y X a x X X a x X + = − + = − Y b y Y Y b y Y X a x X X a (x)X '' ( ) ' ( ) '' ( ) ' 1 2 1 2 b1 (y)Y''+b2 (y)Y'−Y = 0 a1 (x)X''+a2 (x)X'+X = 0