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Separation of variables is a method of solving ordinary and partial differential equations. For an ordinary differential equation (dy)/(dx)=g(x)f(y), (1) where f(y)is nonzero ...

The Ablowitz-Ramani-Segur conjecture states that a nonlinear partial differential equation is solvable by the inverse scattering method only if every nonlinear ordinary ...

A second-order ordinary differential equation of the form

The system of partial differential equations describing fluid flow in the absence of viscosity, given by (partialu)/(partialt)+u·del u=-(del P)/rho, where u is the fluid ...

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 ...

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

Differential geometry is the study of Riemannian manifolds. Differential geometry deals with metrical notions on manifolds, while differential topology deals with nonmetrical ...

A differential ideal I on a manifold M is an ideal in the exterior algebra of differential k-forms on M which is also closed under the exterior derivative d. That is, for any ...

An infinitesimal which is not the differential of an actual function and which cannot be expressed as dz=((partialz)/(partialx))_ydx+((partialz)/(partialy))_xdy, the way an ...

The motivating force of topology, consisting of the study of smooth (differentiable) manifolds. Differential topology deals with nonmetrical notions of manifolds, while ...