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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]
In mathematics, the Laplace transform is a powerful integral transform used to switch a function from the time domain to the s-domain.The Laplace transform can be used in some cases to solve linear differential equations with given initial conditions.
In mathematics, delay differential equations (DDEs) are a type of differential equation in which the derivative of the unknown function at a certain time is given in terms of the values of the function at previous times.
Confluent Hypergeometric Functions can be used to solve the Extended Confluent Hypergeometric Equation whose general form is given as: + (=) = [1] Note that for M = 0 or when the summation involves just one term, it reduces to the conventional Confluent Hypergeometric Equation.
More generally, we can factor a complex m×n matrix A, with m ≥ n, as the product of an m×m unitary matrix Q and an m×n upper triangular matrix R.As the bottom (m−n) rows of an m×n upper triangular matrix consist entirely of zeroes, it is often useful to partition R, or both R and Q:
In numerical linear algebra, the alternating-direction implicit (ADI) method is an iterative method used to solve Sylvester matrix equations.It is a popular method for solving the large matrix equations that arise in systems theory and control, [1] and can be formulated to construct solutions in a memory-efficient, factored form.
A Texas Instruments TI-Nspire calculator that contains a computer algebra system. Computer algebra systems began to appear in the 1960s and evolved out of two quite different sources—the requirements of theoretical physicists and research into artificial intelligence.
Nonlinear ones are of particular interest for their commonality in describing real-world systems and how much more difficult they are to solve compared to linear differential equations. This list presents nonlinear ordinary differential equations that have been named, sorted by area of interest.
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