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The partial differential equation u_t+2uu_x-nuu_(xx)+muu_(xxx)=0.

In two-dimensional bipolar coordinates, Laplace's equation is ((coshv-cosu)^2)/(a^2)((partialF^2)/(partialu^2)+(partialF^2)/(partialv^2))=0, which simplifies to ...

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

The so-called generalized Kadomtsev-Petviashvili-Burgers equation is the partial differential equation ...

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

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.

A Fredholm integral equation of the second kind phi(x)=f(x)+lambdaint_a^bK(x,t)phi(t)dt (1) may be solved as follows. Take phi_0(x) = f(x) (2) phi_1(x) = ...

Whittaker and Watson (1990, pp. 539-540) write Lamé's differential equation for ellipsoidal harmonics of the first kind of the four types as ...

The ordinary differential equation y^('')+k/xy^'+deltae^y=0.