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The inhomogeneous Helmholtz differential equation is del ^2psi(r)+k^2psi(r)=rho(r), (1) where the Helmholtz operator is defined as L^~=del ^2+k^2. The Green's function is ...

In three dimensions, the spherical harmonic differential equation is given by ...

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).

The so-called Malthusian equation is an antiquated term for the equation N(t)=N_0e^(lambdat) describing exponential growth. The constant lambda is sometimes called the ...

Unlike quadratic, cubic, and quartic polynomials, the general quintic cannot be solved algebraically in terms of a finite number of additions, subtractions, multiplications, ...

The partial differential equation u_t+u_(xxx)-6uu_x=0 (1) (Lamb 1980; Zwillinger 1997, p. 175), often abbreviated "KdV." This is a nondimensionalized version of the equation ...

The ordinary differential equation (x^py^')^'+/-x^sigmay^n=0.

Solving the wave equation on a disk gives a solution in terms of Bessel functions.

Poisson's equation is del ^2phi=4pirho, (1) where phi is often called a potential function and rho a density function, so the differential operator in this case is L^~=del ...

Exponentiation is the process of taking a quantity b (the base) to the power of another quantity e (the exponent). This operation most commonly denoted b^e. In TeX, the ...