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A natural equation is an equation which specifies a curve independent of any choice of coordinates or parameterization. The study of natural equations began with the ...

A differential of the form df=P(x,y)dx+Q(x,y)dy (1) is exact (also called a total differential) if intdf is path-independent. This will be true if ...

Solving the wave equation on a disk gives a solution in terms of Bessel functions.

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 ...

The partial differential equation (1-u_t^2)u_(xx)+2u_xu_tu_(xt)-(1+u_x^2)u_(tt)=0.

The partial differential equation u_t=u_(xxx)u^3.

The system of partial differential equations u_t = 1/2u_(xxx)+3uu_x-6ww_x (1) w_t = -w_(xxx)-3uw_x. (2)

The system of partial differential equations U_t=U·U_(xx)+U·LambdaU.

The partial differential equation 2u_(tx)+u_xu_(xx)-u_(yy)=0.

The partial differential equation u_(tt)-u_(xx)-u+u^3=0.