Isocline

The word comes from the Greek words ἴσος (isos), meaning "same", and the κλίνειν (klenein), meaning "make to slope".

Isoclines are often used as a graphical method of solving ordinary differential equations.

In an equation of the form y' = f(x, y), the isoclines are lines in the (x, y) plane obtained by setting f(x, y) equal to a constant.

This gives a series of lines (for different constants) along which the solution curves have the same gradient.

By calculating this gradient for each isocline, the slope field can be visualised; making it relatively easy to sketch approximate solution curves; as in fig. 1.