8.3.6 Systems of ordinary differential equations

Problem: Find the general solution (the first integrals) of the system of differential equations: \[ \frac{d x}{x\left(y^{2}-z^{2}\right)}=\frac{d y}{-y\left(x^{2}+z^{2}\right)}=\frac{d z}{z\left(x^{2}+y^{2}\right)} \text {. } \]