ODE No. 1507

5.59 ODE No. 1507

$(a x + b) x \frac{d^{3}}{d x^{3}} y (x) + (α x + β) \frac{d^{2}}{d x^{2}} y (x) + x \frac{d}{d x} y (x) + y (x) - f (x) = 0$

Mathematica: cpu = 2.446811 (sec), leaf count = 40 $DSolve [x y^{(3)} (x) (a x + b) + (α x + β) y^{″} (x) - f (x) + x y^{'} (x) + y (x) = 0, y (x), x]$

Maple: cpu = 0.468 (sec), leaf count = 1421 ${y (x) = H e u n C (0, \frac{- 2 b + β}{b}, \frac{(2 b + β) a - α b}{a b}, - \frac{b}{a^{2}}, \frac{(4 a - α) b^{2} - α β b + a β^{2}}{2 a b^{2}}, - \frac{a x}{b}) {(a x + b)}^{\frac{(2 b + β) a - α b}{a b}}_C 3 + H e u n C (0, \frac{2 b - β}{b}, \frac{(2 b + β) a - α b}{a b}, - \frac{b}{a^{2}}, \frac{(4 a - α) b^{2} - α β b + a β^{2}}{2 a b^{2}}, - \frac{a x}{b}) x^{\frac{2 b - β}{b}} {(a x + b)}^{\frac{(2 b + β) a - α b}{a b}}_C 2 + {(a x + b)}^{\frac{(2 b + β) a - α b}{a b}} b (- x^{\frac{2 b - β}{b}} \int - (_C 1 + \int f (x) d x) H e u n C (0, \frac{- 2 b + β}{b}, \frac{(2 b + β) a - α b}{a b}, - \frac{b}{a^{2}}, \frac{(4 a - α) b^{2} - α β b + a β^{2}}{2 a b^{2}}, - \frac{a x}{b}) {(a x + b)}^{\frac{(- 3 b - β) a + α b}{a b}} x^{\frac{- 2 b + β}{b}} {(((2 b - β) H e u n C (0, \frac{- 2 b + β}{b}, \frac{(2 b + β) a - α b}{a b}, - \frac{b}{a^{2}}, \frac{(4 a - α) b^{2} - α β b + a β^{2}}{2 a b^{2}}, - \frac{a x}{b}) + a H e u n C P r i m e (0, \frac{- 2 b + β}{b}, \frac{(2 b + β) a - α b}{a b}, - \frac{b}{a^{2}}, \frac{(4 a - α) b^{2} - α β b + a β^{2}}{2 a b^{2}}, - \frac{a x}{b}) x) H e u n C (0, \frac{2 b - β}{b}, \frac{(2 b + β) a - α b}{a b}, - \frac{b}{a^{2}}, \frac{(4 a - α) b^{2} - α β b + a β^{2}}{2 a b^{2}}, - \frac{a x}{b}) - H e u n C (0, \frac{- 2 b + β}{b}, \frac{(2 b + β) a - α b}{a b}, - \frac{b}{a^{2}}, \frac{(4 a - α) b^{2} - α β b + a β^{2}}{2 a b^{2}}, - \frac{a x}{b}) H e u n C P r i m e (0, \frac{2 b - β}{b}, \frac{(2 b + β) a - α b}{a b}, - \frac{b}{a^{2}}, \frac{(4 a - α) b^{2} - α β b + a β^{2}}{2 a b^{2}}, - \frac{a x}{b}) x a)}^{- 1} d x H e u n C (0, \frac{2 b - β}{b}, \frac{(2 b + β) a - α b}{a b}, - \frac{b}{a^{2}}, \frac{(4 a - α) b^{2} - α β b + a β^{2}}{2 a b^{2}}, - \frac{a x}{b}) + H e u n C (0, \frac{- 2 b + β}{b}, \frac{(2 b + β) a - α b}{a b}, - \frac{b}{a^{2}}, \frac{(4 a - α) b^{2} - α β b + a β^{2}}{2 a b^{2}}, - \frac{a x}{b}) \int - (_C 1 + \int f (x) d x) H e u n C (0, \frac{2 b - β}{b}, \frac{(2 b + β) a - α b}{a b}, - \frac{b}{a^{2}}, \frac{(4 a - α) b^{2} - α β b + a β^{2}}{2 a b^{2}}, - \frac{a x}{b}) {(a x + b)}^{\frac{(- 3 b - β) a + α b}{a b}} {(((2 b - β) H e u n C (0, \frac{- 2 b + β}{b}, \frac{(2 b + β) a - α b}{a b}, - \frac{b}{a^{2}}, \frac{(4 a - α) b^{2} - α β b + a β^{2}}{2 a b^{2}}, - \frac{a x}{b}) + a H e u n C P r i m e (0, \frac{- 2 b + β}{b}, \frac{(2 b + β) a - α b}{a b}, - \frac{b}{a^{2}}, \frac{(4 a - α) b^{2} - α β b + a β^{2}}{2 a b^{2}}, - \frac{a x}{b}) x) H e u n C (0, \frac{2 b - β}{b}, \frac{(2 b + β) a - α b}{a b}, - \frac{b}{a^{2}}, \frac{(4 a - α) b^{2} - α β b + a β^{2}}{2 a b^{2}}, - \frac{a x}{b}) - H e u n C (0, \frac{- 2 b + β}{b}, \frac{(2 b + β) a - α b}{a b}, - \frac{b}{a^{2}}, \frac{(4 a - α) b^{2} - α β b + a β^{2}}{2 a b^{2}}, - \frac{a x}{b}) H e u n C P r i m e (0, \frac{2 b - β}{b}, \frac{(2 b + β) a - α b}{a b}, - \frac{b}{a^{2}}, \frac{(4 a - α) b^{2} - α β b + a β^{2}}{2 a b^{2}}, - \frac{a x}{b}) x a)}^{- 1} d x)}$

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