- 期刊
ALTERNATIVE INTEGRATION PROCEDURE FOR SCALE-INVARIANT ORDINARY DIFFERENTIAL EQUATIONS
並列摘要
For an ordinary differential equation invariant under a one-parameter group of scale transformations x →λx, y →λ^(α-1) y', y＂→λ^(α-2) y＂, etc., it is shown by example that an explicit analytical general solution may be obtainable in parametric form in terms of the scale-invariant variable □≡ʃ^x y^(-1/α) dx. This alternative integration may go through, as it does for the example equation y＂= kxy^(-2)y’, in cases for which the customary dependent and independent variables (x^(-α)y) and (ℓn x) do not yield an analytically integrable transformed equation.
延伸閱讀
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