ODE No. 1482

2.1482 ODE No. 1482

Problem in Latex
Mathematica input
Maple input

$a x y (x) - b + 3 y^{″} (x) + 2 x y^{(3)} (x) = 0$ ✗ Mathematica : cpu = 0.459929 (sec), leaf count = 0 , DiﬀerentialRoot result

$\left \{\left \{y(x)\to \text {DifferentialRoot}\left (\{\unicode {f818},\unicode {f817}\}\unicode {f4a1}\left \{-b+\unicode {f817} a \unicode {f818}(\unicode {f817})+3 \unicode {f818}''(\unicode {f817})+2 \unicode {f817} \unicode {f818}^{(3)}(\unicode {f817})=0,\unicode {f818}(1)=c_1,\unicode {f818}'(1)=c_2,\unicode {f818}''(1)=c_3\right \}\right )(x)\right \}\right \}$

✓ Maple : cpu = 0.267 (sec), leaf count = 1616

${y (x) = - \int 2802800 b x ((- 5 / 8_{0} F_{2} (; \frac{13}{6}, 7 / 3; - \frac{a x^{3}}{54}) a x^{3} + \frac{35}{4}_{0} F_{2} (; 7 / 6, 4 / 3; - \frac{a x^{3}}{54}))_{0} F_{2} (; 5 / 6, 7 / 6; - \frac{a x^{3}}{54}) + x^{3}_{0} F_{2} (; \frac{11}{6}, \frac{13}{6}; - \frac{a x^{3}}{54})_{0} F_{2} (; 7 / 6, 4 / 3; - \frac{a x^{3}}{54}) a) {(((- 89180 a^{2} x^{6}_{0} F_{2} (; 8 / 3, \frac{17}{6}; - \frac{a x^{3}}{54}) + 7357350 a x^{3}_{0} F_{2} (; 5 / 3, \frac{11}{6}; - \frac{a x^{3}}{54}) - 24524500_{0} F_{2} (; 2 / 3, 5 / 6; - \frac{a x^{3}}{54}))_{0} F_{2} (; 7 / 6, 4 / 3; - \frac{a x^{3}}{54}) - 3850 a ((5_{0} F_{2} (; \frac{19}{6}, 10 / 3; - \frac{a x^{3}}{54}) a x^{3} - \frac{4095}{2}_{0} F_{2} (; \frac{13}{6}, 7 / 3; - \frac{a x^{3}}{54}))_{0} F_{2} (; 2 / 3, 5 / 6; - \frac{a x^{3}}{54}) + a ((- \frac{91 a x^{3}}{55}_{0} F_{2} (; 8 / 3, \frac{17}{6}; - \frac{a x^{3}}{54}) - 182_{0} F_{2} (; 5 / 3, \frac{11}{6}; - \frac{a x^{3}}{54}))_{0} F_{2} (; \frac{13}{6}, 7 / 3; - \frac{a x^{3}}{54}) + a_{0} F_{2} (; \frac{19}{6}, 10 / 3; - \frac{a x^{3}}{54}) x^{3}_{0} F_{2} (; 5 / 3, \frac{11}{6}; - \frac{a x^{3}}{54})) x^{3}) x^{3})_{0} F_{2} (; 5 / 6, 7 / 6; - \frac{a x^{3}}{54}) + 2200 a (((\frac{392 a x^{3}}{11}_{0} F_{2} (; \frac{17}{6}, \frac{19}{6}; - \frac{a x^{3}}{54}) - 7644_{0} F_{2} (; \frac{11}{6}, \frac{13}{6}; - \frac{a x^{3}}{54}))_{0} F_{2} (; 2 / 3, 5 / 6; - \frac{a x^{3}}{54}) - \frac{1274 a x^{3}}{275} ((_{0} F_{2} (; 8 / 3, \frac{17}{6}; - \frac{a x^{3}}{54}) a x^{3} + 55_{0} F_{2} (; 5 / 3, \frac{11}{6}; - \frac{a x^{3}}{54}))_{0} F_{2} (; \frac{11}{6}, \frac{13}{6}; - \frac{a x^{3}}{54}) - \frac{10 a x^{3}}{13}_{0} F_{2} (; \frac{17}{6}, \frac{19}{6}; - \frac{a x^{3}}{54})_{0} F_{2} (; 5 / 3, \frac{11}{6}; - \frac{a x^{3}}{54})))_{0} F_{2} (; 7 / 6, 4 / 3; - \frac{a x^{3}}{54}) + a_{0} F_{2} (; 2 / 3, 5 / 6; - \frac{a x^{3}}{54}) x^{3} ((_{0} F_{2} (; \frac{19}{6}, 10 / 3; - \frac{a x^{3}}{54}) a x^{3} - 91_{0} F_{2} (; \frac{13}{6}, 7 / 3; - \frac{a x^{3}}{54}))_{0} F_{2} (; \frac{11}{6}, \frac{13}{6}; - \frac{a x^{3}}{54}) - \frac{14 a x^{3}}{11}_{0} F_{2} (; \frac{17}{6}, \frac{19}{6}; - \frac{a x^{3}}{54})_{0} F_{2} (; \frac{13}{6}, 7 / 3; - \frac{a x^{3}}{54}))) x^{3})}^{- 1} d x_{0} F_{2} (; \frac{2}{3}, \frac{5}{6}; - \frac{a x^{3}}{54}) - \int - 2802800 b ((x^{3}_{0} F_{2} (; \frac{11}{6}, \frac{13}{6}; - \frac{a x^{3}}{54}) a - \frac{35}{4}_{0} F_{2} (; 5 / 6, 7 / 6; - \frac{a x^{3}}{54}))_{0} F_{2} (; 2 / 3, 5 / 6; - \frac{a x^{3}}{54}) - 7 / 4 x^{3}_{0} F_{2} (; 5 / 3, \frac{11}{6}; - \frac{a x^{3}}{54})_{0} F_{2} (; 5 / 6, 7 / 6; - \frac{a x^{3}}{54}) a) {(((- 19250 a^{2}_{0} F_{2} (; \frac{19}{6}, 10 / 3; - \frac{a x^{3}}{54}) x^{6} + 7882875_{0} F_{2} (; \frac{13}{6}, 7 / 3; - \frac{a x^{3}}{54}) a x^{3} - 24524500_{0} F_{2} (; 7 / 6, 4 / 3; - \frac{a x^{3}}{54}))_{0} F_{2} (; 5 / 6, 7 / 6; - \frac{a x^{3}}{54}) + 2200 a x^{3} ((\frac{392 a x^{3}}{11}_{0} F_{2} (; \frac{17}{6}, \frac{19}{6}; - \frac{a x^{3}}{54}) - 7644_{0} F_{2} (; \frac{11}{6}, \frac{13}{6}; - \frac{a x^{3}}{54}))_{0} F_{2} (; 7 / 6, 4 / 3; - \frac{a x^{3}}{54}) + a x^{3} ((_{0} F_{2} (; \frac{19}{6}, 10 / 3; - \frac{a x^{3}}{54}) a x^{3} - 91_{0} F_{2} (; \frac{13}{6}, 7 / 3; - \frac{a x^{3}}{54}))_{0} F_{2} (; \frac{11}{6}, \frac{13}{6}; - \frac{a x^{3}}{54}) - \frac{14 a x^{3}}{11}_{0} F_{2} (; \frac{17}{6}, \frac{19}{6}; - \frac{a x^{3}}{54})_{0} F_{2} (; \frac{13}{6}, 7 / 3; - \frac{a x^{3}}{54}))))_{0} F_{2} (; 2 / 3, 5 / 6; - \frac{a x^{3}}{54}) - 10192 a x^{3} (((\frac{35 a x^{3}}{4}_{0} F_{2} (; 8 / 3, \frac{17}{6}; - \frac{a x^{3}}{54}) - \frac{5775}{8}_{0} F_{2} (; 5 / 3, \frac{11}{6}; - \frac{a x^{3}}{54}))_{0} F_{2} (; 7 / 6, 4 / 3; - \frac{a x^{3}}{54}) + \frac{275 a x^{3}}{728} ((_{0} F_{2} (; \frac{19}{6}, 10 / 3; - \frac{a x^{3}}{54}) a x^{3} - 182_{0} F_{2} (; \frac{13}{6}, 7 / 3; - \frac{a x^{3}}{54}))_{0} F_{2} (; 5 / 3, \frac{11}{6}; - \frac{a x^{3}}{54}) - \frac{91 a x^{3}}{55}_{0} F_{2} (; 8 / 3, \frac{17}{6}; - \frac{a x^{3}}{54})_{0} F_{2} (; \frac{13}{6}, 7 / 3; - \frac{a x^{3}}{54})))_{0} F_{2} (; 5 / 6, 7 / 6; - \frac{a x^{3}}{54}) + a ((_{0} F_{2} (; 8 / 3, \frac{17}{6}; - \frac{a x^{3}}{54}) a x^{3} + 55_{0} F_{2} (; 5 / 3, \frac{11}{6}; - \frac{a x^{3}}{54}))_{0} F_{2} (; \frac{11}{6}, \frac{13}{6}; - \frac{a x^{3}}{54}) - \frac{10 a x^{3}}{13}_{0} F_{2} (; \frac{17}{6}, \frac{19}{6}; - \frac{a x^{3}}{54})_{0} F_{2} (; 5 / 3, \frac{11}{6}; - \frac{a x^{3}}{54})) x^{3}_{0} F_{2} (; 7 / 6, 4 / 3; - \frac{a x^{3}}{54})))}^{- 1} d x_{0} F_{2} (; \frac{7}{6}, \frac{4}{3}; - \frac{a x^{3}}{54}) x - \int - 1751750 \sqrt{x} b ((_{0} F_{2} (; \frac{13}{6}, 7 / 3; - \frac{a x^{3}}{54}) a x^{3} - 28_{0} F_{2} (; 7 / 6, 4 / 3; - \frac{a x^{3}}{54}))_{0} F_{2} (; 2 / 3, 5 / 6; - \frac{a x^{3}}{54}) - \frac{14 a x^{3}}{5}_{0} F_{2} (; 7 / 6, 4 / 3; - \frac{a x^{3}}{54})_{0} F_{2} (; 5 / 3, \frac{11}{6}; - \frac{a x^{3}}{54})) {(((- 78400 a^{2}_{0} F_{2} (; \frac{17}{6}, \frac{19}{6}; - \frac{a x^{3}}{54}) x^{6} + 16816800 x^{3}_{0} F_{2} (; \frac{11}{6}, \frac{13}{6}; - \frac{a x^{3}}{54}) a + 24524500_{0} F_{2} (; 5 / 6, 7 / 6; - \frac{a x^{3}}{54}))_{0} F_{2} (; 7 / 6, 4 / 3; - \frac{a x^{3}}{54}) + 19250 a (_{0} F_{2} (; \frac{19}{6}, 10 / 3; - \frac{a x^{3}}{54}) a x^{3} - \frac{819}{2}_{0} F_{2} (; \frac{13}{6}, 7 / 3; - \frac{a x^{3}}{54})) x^{3}_{0} F_{2} (; 5 / 6, 7 / 6; - \frac{a x^{3}}{54}) + 2800 a^{2} x^{6} ((_{0} F_{2} (; \frac{17}{6}, \frac{19}{6}; - \frac{a x^{3}}{54}) a x^{3} + \frac{143}{2}_{0} F_{2} (; \frac{11}{6}, \frac{13}{6}; - \frac{a x^{3}}{54}))_{0} F_{2} (; \frac{13}{6}, 7 / 3; - \frac{a x^{3}}{54}) - \frac{11 a x^{3}}{14}_{0} F_{2} (; \frac{11}{6}, \frac{13}{6}; - \frac{a x^{3}}{54})_{0} F_{2} (; \frac{19}{6}, 10 / 3; - \frac{a x^{3}}{54})))_{0} F_{2} (; 2 / 3, 5 / 6; - \frac{a x^{3}}{54}) - 6370 a x^{3} (((- 14_{0} F_{2} (; 8 / 3, \frac{17}{6}; - \frac{a x^{3}}{54}) a x^{3} + 1155_{0} F_{2} (; 5 / 3, \frac{11}{6}; - \frac{a x^{3}}{54}))_{0} F_{2} (; 5 / 6, 7 / 6; - \frac{a x^{3}}{54}) - 8 / 5 a ((- \frac{10 a x^{3}}{13}_{0} F_{2} (; \frac{17}{6}, \frac{19}{6}; - \frac{a x^{3}}{54}) + 55_{0} F_{2} (; \frac{11}{6}, \frac{13}{6}; - \frac{a x^{3}}{54}))_{0} F_{2} (; 5 / 3, \frac{11}{6}; - \frac{a x^{3}}{54}) + a_{0} F_{2} (; \frac{11}{6}, \frac{13}{6}; - \frac{a x^{3}}{54}) x^{3}_{0} F_{2} (; 8 / 3, \frac{17}{6}; - \frac{a x^{3}}{54})) x^{3})_{0} F_{2} (; 7 / 6, 4 / 3; - \frac{a x^{3}}{54}) + a x^{3} ((- \frac{55 a x^{3}}{91}_{0} F_{2} (; \frac{19}{6}, 10 / 3; - \frac{a x^{3}}{54}) + 110_{0} F_{2} (; \frac{13}{6}, 7 / 3; - \frac{a x^{3}}{54}))_{0} F_{2} (; 5 / 3, \frac{11}{6}; - \frac{a x^{3}}{54}) + a x^{3}_{0} F_{2} (; 8 / 3, \frac{17}{6}; - \frac{a x^{3}}{54})_{0} F_{2} (; \frac{13}{6}, 7 / 3; - \frac{a x^{3}}{54}))_{0} F_{2} (; 5 / 6, 7 / 6; - \frac{a x^{3}}{54})))}^{- 1} d x \sqrt{x}_{0} F_{2} (; \frac{5}{6}, \frac{7}{6}; - \frac{a x^{3}}{54}) +_C 1_{0} F_{2} (; \frac{2}{3}, \frac{5}{6}; - \frac{a x^{3}}{54}) +_C 2_{0} F_{2} (; \frac{7}{6}, \frac{4}{3}; - \frac{a x^{3}}{54}) x +_C 3 \sqrt{x}_{0} F_{2} (; \frac{5}{6}, \frac{7}{6}; - \frac{a x^{3}}{54})}$

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