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3

EDIT: added use of PlotLegends package Use a single Plot with the option Filling Needs["PlotLegends`"]; EffPot[r_, Energy_, AngMom_] := -Energy/r + (AngMom^2 - 1)/(2 r^2) Manipulate[ Plot[{ EffPot[r, Energy, AngMom], (Energy^2 - 1)/2}, {r, 0, 10}, PlotStyle -> { {Thick, RGBColor[0.60, 0.20, 0.40]}, {Thick, RGBColor[0.20, 0.20, ...


3

Interesting equation. It seems to be necessary to use the asymptotic solution as the boundary at $x=x_0$ if you want to solve the equation correctly. Thanks to this answer, we can easily get the series solution at $x=0$ with seriesDSolve: eq1 = 1/5 (y[x] - 2 x y'[x]) == D[(x y'[x])/y[x] + x y[x]^3 D[D[x y'[x], x]/x, x], x]/x; bc1 = y[x] - 2 x y'[x] == 0; ...



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