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Kepler's equation gives the relation between the polar coordinates of a celestial body (such as a planet) and the time elapsed from a given initial point. Kepler's equation ...

A partial differential equation (PDE) is an equation involving functions and their partial derivatives; for example, the wave equation ...

The partial differential equation (1+u_y^2)u_(xx)-2u_xu_yu_(xy)+(1+u_x^2)u_(yy)=0 (correcting a typo in Zwillinger 1997, p. 134).

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 (k,l)-multigrade equation is a Diophantine equation of the form sum_(i=1)^ln_i^j=sum_(i=1)^lm_i^j (1) for j=1, ..., k, where m and n are l-vectors. Multigrade identities ...

The Legendre differential equation is the second-order ordinary differential equation (1-x^2)(d^2y)/(dx^2)-2x(dy)/(dx)+l(l+1)y=0, (1) which can be rewritten ...

The second-order ordinary differential equation y^('')+k/xy^'+epsilony^'y=0.

The partial differential equation del ^2A=-del xE, where del ^2 is the vector Laplacian.

A differential equation is an equation that involves the derivatives of a function as well as the function itself. If partial derivatives are involved, the equation is called ...

A linear congruence equation ax=b (mod m) (1) is solvable iff the congruence b=0 (mod d) (2) with d=GCD(a,m) is the greatest common divisor is solvable. Let one solution to ...