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

The Laguerre differential equation is given by xy^('')+(1-x)y^'+lambday=0. (1) Equation (1) is a special case of the more general associated Laguerre differential equation, ...

To find the motion of a rectangular membrane with sides of length L_x and L_y (in the absence of gravity), use the two-dimensional wave equation ...

A linear recurrence equation is a recurrence equation on a sequence of numbers {x_n} expressing x_n as a first-degree polynomial in x_k with k<n. For example ...

A partial differential diffusion equation of the form (partialU)/(partialt)=kappadel ^2U. (1) Physically, the equation commonly arises in situations where kappa is the ...

The second-order ordinary differential equation (d^2y)/(dx^2)-2x(dy)/(dx)+lambday=0. (1) This differential equation has an irregular singularity at infty. It can be solved ...

An equation proposed by Lambert (1758) and studied by Euler in 1779. x^alpha-x^beta=(alpha-beta)vx^(alpha+beta). (1) When alpha->beta, the equation becomes lnx=vx^beta, (2) ...

Some authors define a general Airy differential equation as y^('')+/-k^2xy=0. (1) This equation can be solved by series solution using the expansions y = ...

A differential-algebraic equation (DAE) is a type of differential equation in which the derivatives are not (in general) expressed explicitly, and typically derivatives of ...

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. ...