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$p$ is $dz/dx$, $q$ is $dz/dy$

I've written down the Charpit's equations:

$\frac{dp}{a}=\frac{dq}{b}=\frac{dz}{3q^2p}=\frac{dx}{q^2}=\frac{dy}{2qp}$

But i'm clueless as to what to do next. I don't know why would anyone find these enjoyable and i'm totally clueless about what these equations would mean in the real world, but anyway, i would appreciate if someone helped me out with this.

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    $\begingroup$ 'I'm clueless as to what to do next'... Solve them \begin{align} dp/a &= dq/b \\ \implies bp &= aq + c_{1} \\ d(p + q)/(a + b) &= dy/2qp \\ \implies \dots \end{align} $\endgroup$
    – mattos
    Dec 27, 2019 at 0:42

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