Algebra

Indeterminate equation

In mathematics, particularly in algebra, an indeterminate equation is an equation for which there is more than one solution. For example, the equation is a simple indeterminate equation, as is . Indeterminate equations cannot be solved uniquely. In fact, in some cases it might even have infinitely many solutions. Some of the prominent examples of indeterminate equations include: Univariate polynomial equation: which has multiple solutions for the variable in the complex plane—unless it can be rewritten in the form . Non-degenerate conic equation: where at least one of the given parameters , , and is non-zero, and and are real variables. Pell's equation: where is a given integer that is not a square number, and in which the variables and are required to be integers. The equation of Pythagorean triples: in which the variables , , and are required to be positive integers. The equation of the Fermat–Catalan conjecture: in which the variables , , are required to be coprime positive integers, and the variables , , and are required to be positive integers satisfying the following equation: (Wikipedia).

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From playlist Linear Second Order Nonhomogeneous Differential Equations: Method of Undetermined Coefficients

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From playlist Method of Undetermined Coefficients, (Nagle Sect4.4)

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From playlist Linear Second Order Nonhomogeneous Differential Equations: Method of Undetermined Coefficients

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From playlist Linear Second Order Nonhomogeneous Differential Equations: Method of Undetermined Coefficients

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This lecture is a part of our online course on introductory structural analysis. Sign up using the following URL: https://courses.structure.education/

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Related pages

Complex plane | Indeterminate form | Parameter | Equation | Pell's equation | Mathematics | Linear algebra | Univariate | Integer | Fermat–Catalan conjecture | Square number | Conic section | Indeterminate (variable) | Algebra | Real number | Pythagorean triple | Indeterminate system