Ordinary differential equations

Ordinary differential equations - Ordinary differential...

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Ordinary differential equations Ordinary differential equations are equations to be solved in which the unknown element is a function, rather than a number, and in which the known information relates that function to its derivatives.
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Few such equations admit an explicit answer, but there is a wealth of qualitative information describing the solutions and their dependence on the defining equation. There are many important classes of differential equations for which detailed information is available. Applications to engineering and the sciences abound. Numerical solutions are actively studied.
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Review of terms for classifying first-order ODEs . Although this really means F(x, y, dy/dx) = 0 for some F of 3 variables, all further adjectives assume the equation has the form dy/dx = f(x,y) for some real-valued f defined on a subset of R^2.
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First-order linear differential equations Definition. The general first-order linear differential equation is dy/dx = g(x) y + h(x) (1) Unless other stated, the function g(x) and h(x) are assumed to be continuous for x.
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Definition. The equation
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Ordinary differential equations - Ordinary differential...

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