I am solving first order differential equation: $$(x_0x_1)' =-8 \dfrac{x_0'}{R},$$ where $x_0=f_0(z)$, $x_1=f_1(z)$, $R=r_1-z(r_1-1)=f_2(z)$ (they are all dependent on $z$, but that is not the same dependency).
Also, here first derivative of all variables is derivative along $z$ axis, for example: $x_0' = \dfrac{\mathrm{d}x_0}{\mathrm{d}z}$. These are my steps in solving equation: $$\dfrac{\mathrm{d}}{\mathrm{d}z}(x_0x_1) = -\dfrac{8}{R}\dfrac{\mathrm{d} x_0}{\mathrm{d}z} \bigg/*\mathrm{d}z$$
$$\mathrm{d}(x_0x_1) = -\dfrac{8}{R}\mathrm{d} x_0 \bigg/ integration$$ $$x_0 x_1 = - \dfrac{8}{R} x_0 + C$$ $$z=1: x_0 = 1, x_1 = 0\qquad\Rightarrow \qquad0 = - \dfrac{8}{R} + C$$ $$C=\dfrac{8}{R}$$ $$x_1 = \dfrac{8}{R} \left( \dfrac{1}{x_0}-1\right)$$ Did I miss something in solving this equation? Because, when I compare numerical and this solution there is some difference.
