常微分方程组求解

①x'=A*[1/(y-x)]*(y/x)

2xx'=2Ay/(y-x)

(x^2)'=2Ay/(y-x)

(B/A)*(x^2)'=2By/(y-x)

②z'=D*[1/(z-y)]*(y/z)

2zz'=2Dy/(z-y)

(z^2)'=2Dy/(z-y)

(C/D)*(z^2)'=2Cy/(z-y)

③y'=B*[1/(y-x)]*(x/y)+C*[1/(z-y)]*(z/y)

2yy'=2Bx/(y-x)+2Cz/(z-y)

(y^2)'=2By/(y-x)-2B+2Cy/(z-y)+2C

③-①-②，(y^2)'-(B/A)*(x^2)'-(C/D)*(z^2)'=2C-2B

[y^2-(B/A)*x^2-(C/D)*z^2]'=2C-2B

y^2-(B/A)*x^2-(C/D)*z^2=(2C-2B)*t+E，其中E是任意常数

当t=0时，x=y=z=x0，则E=(1-B/A-C/D)*x0^2

所以y^2-(B/A)*x^2-(C/D)*z^2=(2C-2B)*t+(1-B/A-C/D)*x0^2

两边同乘以AD

ADy^2-BDx^2-ACz^2=(2ACD-2ABD)*t+(AD-BD-AC)*x0^2