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The partial differential equation 3/4U_y+W_x=0, (1) where W_y+U_t-1/4U_(xxx)+3/2UU_x=0 (2) (Krichever and Novikov 1980; Novikov 1999). Zwillinger (1997, p. 131) and Calogero ...

The scalar form of Laplace's equation is the partial differential equation del ^2psi=0, (1) where del ^2 is the Laplacian. Note that the operator del ^2 is commonly written ...

In a normal n×n Latin square, the entries in each row and column are chosen from a "global" set of n objects. Like a Latin square, a partial Latin square has no two rows or ...

The partial differential equation u_t+u_(xxxxx)+30uu_(xxx)+30u_xu_(xx)+180u^2u_x=0.

A rational function P(x)/Q(x) can be rewritten using what is known as partial fraction decomposition. This procedure often allows integration to be performed on each term ...

The partial differential equation u_t+u_x+uu_x-u_(xxt)=0 (Benjamin et al. 1972; Arvin and Goldstein 1985; Zwillinger 1997, p. 130). A generalized version is given by u_t-del ...

In conical coordinates, Laplace's equation can be written ...

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 ...

An inhomogeneous linear ordinary differential equation with constant coefficients is an ordinary differential equation in which coefficients are constants (i.e., not ...

A homogeneous linear ordinary differential equation with constant coefficients is an ordinary differential equation in which coefficients are constants (i.e., not functions), ...