(Suppose derivatives are with respect to x)
The sum of the first two equations gives .
Integrating it twice and using the initial conditions give (1) .
The difference of the first two equations gives (*).
By using the substitution where , (*) becomes .
Integrating it gives .
Initially, . Since , we can conclude that .
, which is a separable ODE in z.
By using the substitution , it can be solved.
Solving it gives a equation relating and , together with (1), we can determine and .