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An elliptic partial differential equation given by del ^2psi+k^2psi=0, (1) where psi is a scalar function and del ^2 is the scalar Laplacian, or del ^2F+k^2F=0, (2) where F ...

The Baer differential equation is given by while the Baer "wave equation" is (Moon and Spencer 1961, pp. 156-157; Zwillinger 1997, p. 121).

The partial differential equation u_t=del ·[M(u)del ((partialf)/(partialu)-Kdel ^2u)].

The partial differential equation u_(xy)+(alphau_x-betau_y)/(x-y)=0.

The partial differential equation u_t=(1+ia)u_(xx)+(1+ic)u-(1+id)|u|^2u.

The partial differential equation u_t+del ^4u+del ^2u+1/2|del u|^2=0, where del ^2 is the Laplacian, del ^4 is the biharmonic operator, and del is the gradient.

The second-order ordinary differential equation y^('')+k/xy^'+epsilony^'y=0.

The second-order ordinary differential equation y^('')+f(x)y^'+y=0.

The second-order ordinary differential equation satisfied by the Neumann polynomials O_n(x).

The partial differential equation u_t+45u^2u_x+15u_xu_(xx)+15uu_(xxx)+u_(xxxxx)=0.