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The partial differential equation (1-u_t^2)u_(xx)+2u_xu_tu_(xt)-(1+u_x^2)u_(tt)=0.

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

The partial differential equation u_(xx)+(y^2)/(1-(y^2)/(c^2))u_(yy)+yu_y=0.

The second-order ordinary differential equation y^('')+[(alphaeta)/(1+eta)+(betaeta)/((1+eta)^2)+gamma]y=0, where eta=e^(deltax).

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

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).