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\begin{equation}

\frac{\partial b}{\partial x}=\frac{b-c}{c^{2}}\end{equation}

where [itex]b[/itex] and [itex]c[/itex] are both functions of [itex]x[/itex]. However, although

I have a closed form relation between [itex]c[/itex] and [itex]x[/itex], I do not have

such a closed form relation between [itex]b[/itex] and [itex]x[/itex]. Is there any analytic

or numeric way to solve this problem. I want a solution linking [itex]b[/itex],

[itex]c[/itex] and [itex]x[/itex]