Then as I already mentioned

$$

\frac{dx}{a(x,y)}=\frac{dy}{b(x,y)}=\frac{du}{f(x,y,u)}

$$

so if integral curve is parametrized by $\tau$: $dx= a\,d\tau$, $dy=b\,d\tau$ then along this curve $du=f\,d\tau$, we get ODE along integral curve.

Examples of variable coefficients will be considered during tutorial and the next lecture.