ODE No. 1507

2.1507 ODE No. 1507

Problem in Latex
Mathematica input
Maple input

$x y^{(3)} (x) (a x + b) + (α x + β) y^{″} (x) - f (x) + x y^{'} (x) + y (x) = 0$ ✓ Mathematica : cpu = 5.8388 (sec), leaf count = 70099 $Too large to display$ ✓ Maple : cpu = 0.747 (sec), leaf count = 1210

${y (x) = ((b (\int - \frac{(c_{1} + \int f (x) d x) x^{\frac{- 2 b + β}{b}} {(a x + b)}^{\frac{α b + (- 3 b - β) a}{a b}} HeunC (0, \frac{- 2 b + β}{b}, \frac{- α b + (2 b + β) a}{a b}, - \frac{b}{a^{2}}, \frac{a β^{2} - α b β + (4 a - α) b^{2}}{2 a b^{2}}, - \frac{a x}{b})}{a x HeunC (0, \frac{- 2 b + β}{b}, \frac{- α b + (2 b + β) a}{a b}, - \frac{b}{a^{2}}, \frac{a β^{2} - α b β + (4 a - α) b^{2}}{2 a b^{2}}, - \frac{a x}{b}) HeunCPrime (0, \frac{2 b - β}{b}, \frac{- α b + (2 b + β) a}{a b}, - \frac{b}{a^{2}}, \frac{a β^{2} - α b β + (4 a - α) b^{2}}{2 a b^{2}}, - \frac{a x}{b}) + (- a x HeunCPrime (0, \frac{- 2 b + β}{b}, \frac{- α b + (2 b + β) a}{a b}, - \frac{b}{a^{2}}, \frac{a β^{2} - α b β + (4 a - α) b^{2}}{2 a b^{2}}, - \frac{a x}{b}) + (- 2 b + β) HeunC (0, \frac{- 2 b + β}{b}, \frac{- α b + (2 b + β) a}{a b}, - \frac{b}{a^{2}}, \frac{a β^{2} - α b β + (4 a - α) b^{2}}{2 a b^{2}}, - \frac{a x}{b})) HeunC (0, \frac{2 b - β}{b}, \frac{- α b + (2 b + β) a}{a b}, - \frac{b}{a^{2}}, \frac{a β^{2} - α b β + (4 a - α) b^{2}}{2 a b^{2}}, - \frac{a x}{b})} d x) + c_{2}) x^{\frac{2 b - β}{b}} HeunC (0, \frac{2 b - β}{b}, \frac{- α b + (2 b + β) a}{a b}, - \frac{b}{a^{2}}, \frac{a β^{2} - α b β + (4 a - α) b^{2}}{2 a b^{2}}, - \frac{a x}{b}) - (b (\int - \frac{(c_{1} + \int f (x) d x) {(a x + b)}^{\frac{α b + (- 3 b - β) a}{a b}} HeunC (0, \frac{2 b - β}{b}, \frac{- α b + (2 b + β) a}{a b}, - \frac{b}{a^{2}}, \frac{a β^{2} - α b β + (4 a - α) b^{2}}{2 a b^{2}}, - \frac{a x}{b})}{a x HeunC (0, \frac{- 2 b + β}{b}, \frac{- α b + (2 b + β) a}{a b}, - \frac{b}{a^{2}}, \frac{a β^{2} - α b β + (4 a - α) b^{2}}{2 a b^{2}}, - \frac{a x}{b}) HeunCPrime (0, \frac{2 b - β}{b}, \frac{- α b + (2 b + β) a}{a b}, - \frac{b}{a^{2}}, \frac{a β^{2} - α b β + (4 a - α) b^{2}}{2 a b^{2}}, - \frac{a x}{b}) + (- a x HeunCPrime (0, \frac{- 2 b + β}{b}, \frac{- α b + (2 b + β) a}{a b}, - \frac{b}{a^{2}}, \frac{a β^{2} - α b β + (4 a - α) b^{2}}{2 a b^{2}}, - \frac{a x}{b}) + (- 2 b + β) HeunC (0, \frac{- 2 b + β}{b}, \frac{- α b + (2 b + β) a}{a b}, - \frac{b}{a^{2}}, \frac{a β^{2} - α b β + (4 a - α) b^{2}}{2 a b^{2}}, - \frac{a x}{b})) HeunC (0, \frac{2 b - β}{b}, \frac{- α b + (2 b + β) a}{a b}, - \frac{b}{a^{2}}, \frac{a β^{2} - α b β + (4 a - α) b^{2}}{2 a b^{2}}, - \frac{a x}{b})} d x) - c_{3}) HeunC (0, \frac{- 2 b + β}{b}, \frac{- α b + (2 b + β) a}{a b}, - \frac{b}{a^{2}}, \frac{a β^{2} - α b β + (4 a - α) b^{2}}{2 a b^{2}}, - \frac{a x}{b})) {(a x + b)}^{\frac{- α b + (2 b + β) a}{a b}}}$

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