Analytic Solutions of Algebraic Differential Equations
Copyright policy )Analytic Solutions of Algebraic Differential Equations
For special polynomials $f_2 (w)$, $f_1 (w)$, $f_0 (w)$ in w with analytic coefficients, the equation $f_2 (w)w'^2 + f_1 (w)w' + f_0 (w) = 0$ has appeared many times in the literature. Frequently, the equation is irreducible, $\deg f_2 = 0$, $\deg f_1 \leqq 2$, $\deg f_0 \leqq 4$, and either $4f_2 f_0 - f_1^2 $ has a multiple root or its degree is $ \leqq 2$. Under these conditions, there is an algebraic transformation to simplify the equation. This paper motivates the transformation and illustrates its effectiveness in diverse situations.
analytic solutions, Analytical theory of ordinary differential equations: series, transformations, transforms, operational calculus, etc., algebraic differential equations
analytic solutions, Analytical theory of ordinary differential equations: series, transformations, transforms, operational calculus, etc., algebraic differential equations
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