Solving nonlinear ODE system with continuous Newton method

Is anyone knows how to apply continuous Newton method for solving nonlinear ODE systems? For example let the system is:

$$\left|\begin{array}{cc} y'= \frac{z}{x} \\ z'= \frac{z(y+2z-1)}{x(y-1)}\end{array}\right.$$

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Is $x$ the dependent variable? –  Jerry Gagelman Aug 29 '12 at 12:46
I think so. It's not mentioned in the text. –  Владислав Найденов Aug 29 '12 at 21:10
Could anyone can help? –  Владислав Найденов Sep 6 '12 at 9:23