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The equation of motion for a membrane shaped as a right isosceles triangle of length c on a side and with the sides oriented along the positive x and y axes is given by where ...

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

The system of partial differential equations del ^2s-(|a|^2+1)s = 0 (1) del ^2a-del (del ·a)-s^2a = a. (2)

A Diophantine equation is an equation in which only integer solutions are allowed. Hilbert's 10th problem asked if an algorithm existed for determining whether an arbitrary ...

The Fredholm integral equation of the second kind f(x)=1+1/piint_(-1)^1(f(t))/((x-t)^2+1)dt that arises in electrostatics (Love 1949, Fox and Goodwin 1953, and Abbott 2002).

A second-order ordinary differential equation d/(dx)[p(x)(dy)/(dx)]+[lambdaw(x)-q(x)]y=0, where lambda is a constant and w(x) is a known function called either the density or ...

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

Let f(x,y) be a homogeneous function of order n so that f(tx,ty)=t^nf(x,y). (1) Then define x^'=xt and y^'=yt. Then nt^(n-1)f(x,y) = ...

A number D that possesses no common divisor with a prime number p is either a quadratic residue or nonresidue of p, depending whether D^((p-1)/2) is congruent mod p to +/-1.

The Machin-like formula 1/4pi=cot^(-1)(2)+cot^(-1)(3). The other 2-term Machin-like formulas are Hermann's formula, hutton's formula, and Machin's formula.