Let Γ be a family of plane curves.  The isocline of Γ is the locus of the points, in which all members of Γ have an equal slope.

If the family Γ has the differential equationMathworldPlanetmath


then the equation of any isocline of Γ has the form


where K is .

For example, the family


of exponentialPlanetmathPlanetmath ( curves satisfies the differential equation  dydx=CeCx  or  dydx=Cy,  whence the isoclines are  Cy=K,  i.e. they are horizontal lines.

Title isocline
Canonical name Isocline
Date of creation 2013-03-22 18:05:52
Last modified on 2013-03-22 18:05:52
Owner pahio (2872)
Last modified by pahio (2872)
Numerical id 6
Author pahio (2872)
Entry type Definition
Classification msc 53A25
Classification msc 53A04
Classification msc 51N05
Related topic OrthogonalCurves