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The areas of the regions illustrated above can be found from the equations A+4B+4C=1 (1) A+3B+2C=1/4pi. (2) Since we want to solve for three variables, we need a third ...

For a linear homogeneous ordinary differential equation, if y_1(x) and y_2(x) are solutions, then so is y_1(x)+y_2(x).

The triangle transformation principle gives rules for transforming equations involving an incircle to equations about excircles.

Given a nonhomogeneous ordinary differential equation, select a differential operator which will annihilate the right side, and apply it to both sides. Find the solution to ...

In general, polynomial equations higher than fourth degree are incapable of algebraic solution in terms of a finite number of additions, subtractions, multiplications, ...

An algebraic surface with affine equation P_d(x_1,x_2)+T_d(x_3)=0, (1) where T_d(x) is a Chebyshev polynomial of the first kind and P_d(x_1,x_2) is a polynomial defined by ...

Adding a damping force proportional to x^. to the equation of simple harmonic motion, the first derivative of x with respect to time, the equation of motion for damped simple ...

The octahedral equation, by way of analogy with the icosahedral equation, is a set of related equations derived from the projective geometry of the octahedron. Consider an ...

A recursive sequence {f(n)}_n, also known as a recurrence sequence, is a sequence of numbers f(n) indexed by an integer n and generated by solving a recurrence equation. The ...

A singular point of an algebraic curve is a point where the curve has "nasty" behavior such as a cusp or a point of self-intersection (when the underlying field K is taken as ...