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The partial differential equation u_t+2uu_x-nuu_(xx)+muu_(xxx)=0.

The partial differential equation P_t=P_(xx)-uP_x+partial/(partialx){[u-F(x)]P}.

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 partial differential equation (Cole and Cook 1986, p. 34; Zwillinger 1997, p. 134).

The second-order ordinary differential equation y^('')+[alpha/(cosh^2(ax))+betatanh(ax)+gamma]y=0.

The ordinary differential equation

A partial differential equation of second-order, i.e., one of the form Au_(xx)+2Bu_(xy)+Cu_(yy)+Du_x+Eu_y+F=0, (1) is called parabolic if the matrix Z=[A B; B C] (2) ...

The partial differential equation u_t=del ·(u^mdel u).

The partial differential equation u_(tt)-u_(xx)=epsilon(u_t-u_t^3).

The method for solving the Goursat problem and Cauchy problem for linear hyperbolic partial differential equations using a Riemann function.