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

An ordinary differential equation of order n is an equation of the form F(x,y,y^',...,y^((n)))=0.

The ordinary differential equation

The second-order ordinary differential equation y^('')-[(M^2-1/4+K^2-2MKcosx)/(sin^2x)+(sigma+K^2+1/4)]y=0.

The second-order ordinary differential equation y^('')=y^(3/2)x^(-1/2).

The partial differential equation iu_t+[(1+|u|^2u)^(-1/2)u]_(xx)=0.

The partial differential equation u_t+u_x+uu_x-u_(xxt)=0 (Benjamin et al. 1972; Arvin and Goldstein 1985; Zwillinger 1997, p. 130). A generalized version is given by u_t-del ...

The second-order ordinary differential equation x^2(d^2y)/(dx^2)+x(dy)/(dx)-(x^2+n^2)y=0. (1) The solutions are the modified Bessel functions of the first and second kinds, ...

The modified spherical Bessel differential equation is given by the spherical Bessel differential equation with a negative separation constant, ...

The system of partial differential equations u_t = (u^2-u_x+2v)_x (1) v_y = (2uv+v_x)_x. (2)