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The Baer differential equation is given by while the Baer "wave equation" is (Moon and Spencer 1961, pp. 156-157; Zwillinger 1997, p. 121).

Partial differential equation boundary conditions which give the value of the function on a surface, e.g., T=f(r,t).

The second-order ordinary differential equation (x^2y^')^'+x^2y^n=0.

The third-order ordinary differential equation y^(''')+alphayy^('')+beta(1-y^('2))=0.

The partial differential equation w_t-6(w+epsilon^2w^2)w_x+w_(xxx)=0, which can also be rewritten (w)_t+(-3w^2-2epsilon^2w^3+w_(xx))_x=0.

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

In bipolar coordinates, the Helmholtz differential equation is not separable, but Laplace's equation is.

The Helmholtz differential equation is not separable in bispherical coordinates.

The Helmholtz differential equation is not separable in toroidal coordinates

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 hyperbolic if the matrix Z=[A B; B C] (2) ...