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In mathematics, an ordinary differential equation (ODE) is a differential equation (DE) dependent on only a single independent variable. As with any other DE, its unknown(s) consists of one (or more) function (s) and involves the derivatives of those functions. [ 1 ]
In mathematics, the Lambert W function, also called the omega function or product logarithm, [1] is a multivalued function, namely the branches of the converse relation of the function f(w) = we w, where w is any complex number and e w is the exponential function. The function is named after Johann Lambert, who considered a related problem in 1758.
Consider a linear non-homogeneous ordinary differential equation of the form = + (+) = where () denotes the i-th derivative of , and denotes a function of .. The method of undetermined coefficients provides a straightforward method of obtaining the solution to this ODE when two criteria are met: [2]
Ordinary differential equations occur in many scientific disciplines, including physics, chemistry, biology, and economics. [1] In addition, some methods in numerical partial differential equations convert the partial differential equation into an ordinary differential equation, which must then be solved.
WolframAlpha (/ ˈ w ʊ l f. r əm-/ WUULf-rəm-) is an answer engine developed by Wolfram Research. [3] It is offered as an online service that answers factual queries by computing answers from externally sourced data.
In mathematics, the Gaussian or ordinary hypergeometric function 2 F 1 (a,b;c;z) is a special function represented by the hypergeometric series, that includes many other special functions as specific or limiting cases. It is a solution of a second-order linear ordinary differential equation (ODE).
This list of mathematical series contains formulae for finite and infinite sums. It can be used in conjunction with other tools for evaluating sums. Here, is taken to have the value
Xcas can solve differential equations. Xcas is a user interface to Giac , which is an open source [ 2 ] computer algebra system (CAS) for Windows , macOS and Linux among many other platforms. Xcas is written in C++ . [ 3 ]
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