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The partial differential equation del ^2u+lambda^2sinhu=0, where del ^2 is the Laplacian (Ting et al. 1987; Zwillinger 1997, p. 135).

The partial differential equation u_(xy)+alphau_x+betau_y+gammau_xu_y=0.

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

The partial differential equation u_(yy)=yu_(xx).

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

As a consequence of Matiyasevich's refutation of Hilbert's 10th problem, it can be proved that there does not exist a general algorithm for solving a general quartic ...

The Clebsch diagonal cubic is a cubic algebraic surface given by the equation x_0^3+x_1^3+x_2^3+x_3^3+x_4^3=0, (1) with the added constraint x_0+x_1+x_2+x_3+x_4=0. (2) The ...

Find a square number x^2 such that, when a given integer h is added or subtracted, new square numbers are obtained so that x^2+h=a^2 (1) and x^2-h=b^2. (2) This problem was ...

The curve formed by the intersection of a cylinder and a sphere is known as Viviani's curve. The problem of finding the lateral surface area of a cylinder of radius r ...

For an ellipse with parametric equations x = acost (1) y = bsint, (2) the negative pedal curve with respect to the origin has parametric equations x_n = ...