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A second-order partial differential equation, i.e., one of the form Au_(xx)+2Bu_(xy)+Cu_(yy)+Du_x+Eu_y+F=0, (1) is called elliptic if the matrix Z=[A B; B C] (2) is positive ...

A Fredholm integral equation of the first kind is an integral equation of the form f(x)=int_a^bK(x,t)phi(t)dt, (1) where K(x,t) is the kernel and phi(t) is an unknown ...

The partial differential equation u_(xy)+(N(u_x+u_y))/(x+y)=0.

The Helmholtz differential equation is not separable in toroidal coordinates

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

The smallest positive composite number and the first even perfect square. Four is the smallest even number appearing in a Pythagorean triple: 3, 4, 5. In the numerology of ...

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.