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The partial differential equation partial/(partialx)(u_t+uu_x+1/2u_(xxx)+u/(2t))+(3alpha^2)/(2t^2)u_(yy)=0 which arises in the study of water waves.

A self-adjoint elliptic differential operator defined somewhat technically as Delta=ddelta+deltad, where d is the exterior derivative and d and delta are adjoint to each ...

In two-dimensional bipolar coordinates, Laplace's equation is ((coshv-cosu)^2)/(a^2)((partialF^2)/(partialu^2)+(partialF^2)/(partialv^2))=0, which simplifies to ...

The ordinary differential equation y^('')+(1-|y|)y^'+y=0.

Partial differential equation boundary conditions which give the normal derivative on a surface.

The partial differential equation u_(xx)=au_(tt)+bu_t+cu.

Solution of a system of second-order homogeneous ordinary differential equations with constant coefficients of the form (d^2x)/(dt^2)+bx=0, where b is a positive definite ...

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 ...

A determinant used to determine in which coordinate systems the Helmholtz differential equation is separable (Morse and Feshbach 1953). A determinant S=|Phi_(mn)|=|Phi_(11) ...

The study, first developed by Boole, of shift-invariant operators which are polynomials in the differential operator D^~. Heaviside calculus can be used to solve any ordinary ...