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The partial differential equation u_t=Du_(xx)+u-u^2.

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

The second-order ordinary differential equation (1+x^2)^2y^('')+lambday=0 (Hille 1969, p. 357; Zwillinger 1997, p. 122).

A collection of equations satisfies the Hasse principle if, whenever one of the equations has solutions in R and all the Q_p, then the equations have solutions in the ...

Hilbert-Schmidt theory is the study of linear integral equations of the Fredholm type with symmetric integral kernels K(x,t)=K(t,x).

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.