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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 equation f(x_n|x_s)=int_(-infty)^inftyf(x_n|x_r)f(x_r|x_s)dx_r which gives the transitional densities of a Markov sequence. Here, n>r>s are any integers (Papoulis 1984, ...

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

The solution to the differential equation [D^(2v)+alphaD^v+betaD^0]y(t)=0 (1) is y(t)={e_alpha(t)-e_beta(t) for alpha!=beta; ...

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

The partial differential equation u_t=u_(xxx)u^3.

The second-order ordinary differential equation (Moon and Spencer 1961, p. 157; Zwillinger 1997, p. 166).

The system of partial differential equations u_t = 1/2u_(xxx)+3uu_x-6ww_x (1) w_t = -w_(xxx)-3uw_x. (2)

The system of partial differential equations U_t=U·U_(xx)+U·LambdaU.

The partial differential equation 2u_(tx)+u_xu_(xx)-u_(yy)=0.