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An natural equation which expresses a curve in terms of its arc length s and tangential angle phi.

An Cesàro equation is a natural equation which expresses a curve in terms of its arc length function s(t) and radius of curvature rho(t) (or equivalently, the curvature ...

rho_(n+1)(x)=intrho_n(y)delta[x-M(y)]dy, where delta(x) is a delta function, M(x) is a map, and rho is the natural invariant.

The partial differential equation u_(yy)=yu_(xx).

The ordinary differential equation y=xf(y^')+g(y^'), where y^'=dy/dx and f and g are given functions. This equation is sometimes also known as Lagrange's equation (Zwillinger ...

The second-order ordinary differential equation y^('')+[A+Bcos(2x)+Ccos(4x)]y=0.

A partial differential equation which appears in differential geometry and relativistic field theory. Its name is a wordplay on its similar form to the Klein-Gordon equation. ...

A second-order ordinary differential equation d/(dx)[p(x)(dy)/(dx)]+[lambdaw(x)-q(x)]y=0, where lambda is a constant and w(x) is a known function called either the density or ...

The second-order ordinary differential equation y^('')+alpha(x)y^'+x^2y^n=0.

A second-order ordinary differential equation of the form