ODE No. 1407

2.1407 ODE No. 1407

$y^{″} (x) = - y^{'} (x) (\frac{b1 (- al1 - bl1 + 1)}{b1 x - a1} + \frac{b2 (- al2 - bl2 + 1)}{b2 x - a2} + \frac{b3 (- al3 - bl3 + 1)}{b3 x - a3}) - \frac{y (x) (\frac{al1 bl1 (a1 b2 - a2 b1) (a3 b1 - a1 b3)}{b1 x - a1} + \frac{al2 bl2 (a1 b2 - a2 b1) (a2 b3 - a3 b2)}{b2 x - a2} + \frac{al3 bl3 (a3 b1 - a1 b3) (a2 b3 - a3 b2)}{b3 x - a3})}{(b1 x - a1) (b2 x - a2) (b3 x - a3)}$ ✗ Mathematica : cpu = 299.997 (sec), leaf count = 0 , timed out

$Aborted

✓ Maple : cpu = 2.914 (sec), leaf count = 2907

${y (x) =_C 1 H e u n G (\frac{b 2 (a 1 b 3 - a 3 b 1)}{b 3 (a 1 b 2 - b 1 a 2)}, - \frac{1}{4 b 3 (a 1 b 2 - b 1 a 2)} (((2 b 2 (a 1 b 3 - a 3 b 1) \sqrt{{a l 2}^{2} + 6 a l 2 b l 2 + {b l 2}^{2}} + (4 a 1 b 3 - 2 a 3 b 1) b 2 - 2 a 2 b 1 b 3) \sqrt{{a l 1}^{2} + 6 a l 1 b l 1 + {b l 1}^{2}} - 2 b 2 (a 1 b 3 - a 3 b 1) \sqrt{{a l 2}^{2} + 6 a l 2 b l 2 + {b l 2}^{2}} + (2 a 1 ((- 4 b l 1 + b l 2 + b l 3 + a l 2 + a l 3 - 2) a l 1 + (b l 2 + b l 3 + a l 2 + a l 3 - 2) b l 1 - b l 2 - b l 3 - a l 2 - a l 3) b 3 - 2 a 3 ((- 2 b l 1 + b l 2 + a l 2 - 1) a l 1 + (- 1 + a l 2 + b l 2) b l 1 + 2 a l 3 b l 3 + (- 2 b l 2 - 1) a l 2 - b l 2) b 1) b 2 - 2 b 1 ((- 2 b l 1 + b l 3 + a l 3 - 1) a l 1 + (- 1 + a l 3 + b l 3) b l 1 + (- 2 b l 3 - 1) a l 3 + 2 a l 2 b l 2 - b l 3) a 2 b 3) \sqrt{{a l 1}^{2} + (2 a l 2 + 2 a l 3 + 2 b l 1 + 2 b l 2 + 2 b l 3 - 4) a l 1 + {a l 2}^{2} + (2 a l 3 + 2 b l 1 + 2 b l 2 + 2 b l 3 - 4) a l 2 + 2 {a l 3}^{2} + (2 b l 1 + 2 b l 2 + 8 b l 3 - 4) a l 3 + {b l 1}^{2} + (2 b l 2 + 2 b l 3 - 4) b l 1 + {b l 2}^{2} + (2 b l 3 - 4) b l 2 + 2 {b l 3}^{2} - 4 b l 3 + 2 \sqrt{({a l 3}^{2} + 6 a l 3 b l 3 + {b l 3}^{2}) {(- 2 + a l 1 + a l 2 + a l 3 + b l 1 + b l 2 + b l 3)}^{2}} + 4} + (a 1 b 2 - b 1 a 2) ((2 \sqrt{{a l 1}^{2} + 6 a l 1 b l 1 + {b l 1}^{2}} - 2) \sqrt{({a l 3}^{2} + 6 a l 3 b l 3 + {b l 3}^{2}) {(- 2 + a l 1 + a l 2 + a l 3 + b l 1 + b l 2 + b l 3)}^{2}} - {({a l 1}^{2} + 6 a l 1 b l 1 + {b l 1}^{2})}^{\frac{3}{2}} + ({a l 1}^{2} + 6 a l 1 b l 1 + 2 {a l 3}^{2} + 12 a l 3 b l 3 + {b l 1}^{2} + 2 {b l 3}^{2}) \sqrt{{a l 1}^{2} + 6 a l 1 b l 1 + {b l 1}^{2}} - 2 {b l 3}^{2} - 12 a l 3 b l 3 - 2 {a l 3}^{2}) b 3) \frac{1}{\sqrt{{a l 1}^{2} + (2 a l 2 + 2 a l 3 + 2 b l 1 + 2 b l 2 + 2 b l 3 - 4) a l 1 + {a l 2}^{2} + (2 a l 3 + 2 b l 1 + 2 b l 2 + 2 b l 3 - 4) a l 2 + 2 {a l 3}^{2} + (2 b l 1 + 2 b l 2 + 8 b l 3 - 4) a l 3 + {b l 1}^{2} + (2 b l 2 + 2 b l 3 - 4) b l 1 + {b l 2}^{2} + (2 b l 3 - 4) b l 2 + 2 {b l 3}^{2} - 4 b l 3 + 2 \sqrt{({a l 3}^{2} + 6 a l 3 b l 3 + {b l 3}^{2}) {(- 2 + a l 1 + a l 2 + a l 3 + b l 1 + b l 2 + b l 3)}^{2}} + 4}}, - \frac{1}{2} \sqrt{{a l 1}^{2} + 6 a l 1 b l 1 + {b l 1}^{2}} + \frac{1}{2} \sqrt{{a l 2}^{2} + 6 a l 2 b l 2 + {b l 2}^{2}} + 1 + \frac{1}{2} \sqrt{{a l 1}^{2} + (2 a l 2 + 2 a l 3 + 2 b l 1 + 2 b l 2 + 2 b l 3 - 4) a l 1 + {a l 2}^{2} + (2 a l 3 + 2 b l 1 + 2 b l 2 + 2 b l 3 - 4) a l 2 + 2 {a l 3}^{2} + (2 b l 1 + 2 b l 2 + 8 b l 3 - 4) a l 3 + {b l 1}^{2} + (2 b l 2 + 2 b l 3 - 4) b l 1 + {b l 2}^{2} + (2 b l 3 - 4) b l 2 + 2 {b l 3}^{2} - 4 b l 3 + 2 \sqrt{({a l 3}^{2} + 6 a l 3 b l 3 + {b l 3}^{2}) {(- 2 + a l 1 + a l 2 + a l 3 + b l 1 + b l 2 + b l 3)}^{2}} + 4}, - \frac{1}{2} ((\sqrt{{a l 1}^{2} + 6 a l 1 b l 1 + {b l 1}^{2}} - \sqrt{{a l 2}^{2} + 6 a l 2 b l 2 + {b l 2}^{2}} - 2) \sqrt{{a l 1}^{2} + (2 a l 2 + 2 a l 3 + 2 b l 1 + 2 b l 2 + 2 b l 3 - 4) a l 1 + {a l 2}^{2} + (2 a l 3 + 2 b l 1 + 2 b l 2 + 2 b l 3 - 4) a l 2 + 2 {a l 3}^{2} + (2 b l 1 + 2 b l 2 + 8 b l 3 - 4) a l 3 + {b l 1}^{2} + (2 b l 2 + 2 b l 3 - 4) b l 1 + {b l 2}^{2} + (2 b l 3 - 4) b l 2 + 2 {b l 3}^{2} - 4 b l 3 + 2 \sqrt{({a l 3}^{2} + 6 a l 3 b l 3 + {b l 3}^{2}) {(- 2 + a l 1 + a l 2 + a l 3 + b l 1 + b l 2 + b l 3)}^{2}} + 4} + (2 a l 1 + 2 a l 2 - 4 a l 3 + 2 b l 1 + 2 b l 2 - 4) b l 3 + (a l 1 + a l 2 + b l 1 + b l 2 - 2) (a l 1 + a l 2 + 2 a l 3 + b l 1 + b l 2 - 2)) \frac{1}{\sqrt{{a l 1}^{2} + (2 a l 2 + 2 a l 3 + 2 b l 1 + 2 b l 2 + 2 b l 3 - 4) a l 1 + {a l 2}^{2} + (2 a l 3 + 2 b l 1 + 2 b l 2 + 2 b l 3 - 4) a l 2 + 2 {a l 3}^{2} + (2 b l 1 + 2 b l 2 + 8 b l 3 - 4) a l 3 + {b l 1}^{2} + (2 b l 2 + 2 b l 3 - 4) b l 1 + {b l 2}^{2} + (2 b l 3 - 4) b l 2 + 2 {b l 3}^{2} - 4 b l 3 + 2 \sqrt{({a l 3}^{2} + 6 a l 3 b l 3 + {b l 3}^{2}) {(- 2 + a l 1 + a l 2 + a l 3 + b l 1 + b l 2 + b l 3)}^{2}} + 4}}, 1 - \sqrt{{a l 1}^{2} + 6 a l 1 b l 1 + {b l 1}^{2}}, 1 + \sqrt{{a l 2}^{2} + 6 a l 2 b l 2 + {b l 2}^{2}}, \frac{b 2 (- b 1 x + a 1)}{a 1 b 2 - b 1 a 2}) {(b 1 x - a 1)}^{\frac{a l 1}{2} + \frac{b l 1}{2} - \frac{1}{2} \sqrt{{a l 1}^{2} + 6 a l 1 b l 1 + {b l 1}^{2}}} {(b 2 x - a 2)}^{\frac{a l 2}{2} + \frac{b l 2}{2} + \frac{1}{2} \sqrt{{a l 2}^{2} + 6 a l 2 b l 2 + {b l 2}^{2}}} {(b 3 x - a 3)}^{\frac{1}{2} ((a l 3 + b l 3) \sqrt{(2 a l 1 + 2 a l 2 + 2 a l 3 + 2 b l 1 + 2 b l 2 + 2 b l 3 - 4) \sqrt{{a l 3}^{2} + 6 a l 3 b l 3 + {b l 3}^{2}} + 2 {b l 3}^{2} + (2 a l 1 + 2 a l 2 + 8 a l 3 + 2 b l 1 + 2 b l 2 - 4) b l 3 + {b l 2}^{2} + (2 a l 1 + 2 a l 2 + 2 a l 3 + 2 b l 1 - 4) b l 2 + {b l 1}^{2} + (2 a l 1 + 2 a l 2 + 2 a l 3 - 4) b l 1 + 2 {a l 3}^{2} + (2 a l 1 + 2 a l 2 - 4) a l 3 + {(a l 1 + a l 2 - 2)}^{2}} + (- 2 + a l 1 + a l 2 + a l 3 + b l 1 + b l 2 + b l 3) \sqrt{{a l 3}^{2} + 6 a l 3 b l 3 + {b l 3}^{2}} + {a l 3}^{2} + 6 a l 3 b l 3 + {b l 3}^{2}) \frac{1}{\sqrt{(2 a l 1 + 2 a l 2 + 2 a l 3 + 2 b l 1 + 2 b l 2 + 2 b l 3 - 4) \sqrt{{a l 3}^{2} + 6 a l 3 b l 3 + {b l 3}^{2}} + 2 {b l 3}^{2} + (2 a l 1 + 2 a l 2 + 8 a l 3 + 2 b l 1 + 2 b l 2 - 4) b l 3 + {b l 2}^{2} + (2 a l 1 + 2 a l 2 + 2 a l 3 + 2 b l 1 - 4) b l 2 + {b l 1}^{2} + (2 a l 1 + 2 a l 2 + 2 a l 3 - 4) b l 1 + 2 {a l 3}^{2} + (2 a l 1 + 2 a l 2 - 4) a l 3 + {(a l 1 + a l 2 - 2)}^{2}}}} +_C 2 H e u n G (\frac{b 2 (a 1 b 3 - a 3 b 1)}{b 3 (a 1 b 2 - b 1 a 2)}, \frac{1}{4 b 3 (a 1 b 2 - b 1 a 2)} (- (- 2 (\sqrt{{a l 2}^{2} + 6 a l 2 b l 2 + {b l 2}^{2}} a 1 b 2 b 3 - \sqrt{{a l 2}^{2} + 6 a l 2 b l 2 + {b l 2}^{2}} a 3 b 1 b 2 + 2 a 1 b 2 b 3 - a 2 b 1 b 3 - a 3 b 1 b 2) \sqrt{{a l 1}^{2} + 6 a l 1 b l 1 + {b l 1}^{2}} - 2 b 2 (a 1 b 3 - a 3 b 1) \sqrt{{a l 2}^{2} + 6 a l 2 b l 2 + {b l 2}^{2}} + (2 a 1 ((- 4 b l 1 + b l 2 + b l 3 + a l 2 + a l 3 - 2) a l 1 + (b l 2 + b l 3 + a l 2 + a l 3 - 2) b l 1 - b l 2 - b l 3 - a l 2 - a l 3) b 2 - 2 b 1 ((- 2 b l 1 + b l 3 + a l 3 - 1) a l 1 + (- 1 + a l 3 + b l 3) b l 1 + (- 2 b l 3 - 1) a l 3 + 2 a l 2 b l 2 - b l 3) a 2) b 3 - 2 ((- 2 b l 1 + b l 2 + a l 2 - 1) a l 1 + (- 1 + a l 2 + b l 2) b l 1 + 2 a l 3 b l 3 + (- 2 b l 2 - 1) a l 2 - b l 2) b 2 b 1 a 3) \sqrt{{a l 1}^{2} + (2 a l 2 + 2 a l 3 + 2 b l 1 + 2 b l 2 + 2 b l 3 - 4) a l 1 + {a l 2}^{2} + (2 a l 3 + 2 b l 1 + 2 b l 2 + 2 b l 3 - 4) a l 2 + 2 {a l 3}^{2} + (2 b l 1 + 2 b l 2 + 8 b l 3 - 4) a l 3 + {b l 1}^{2} + (2 b l 2 + 2 b l 3 - 4) b l 1 + {b l 2}^{2} + (2 b l 3 - 4) b l 2 + 2 {b l 3}^{2} - 4 b l 3 + 2 \sqrt{({a l 3}^{2} + 6 a l 3 b l 3 + {b l 3}^{2}) {(- 2 + a l 1 + a l 2 + a l 3 + b l 1 + b l 2 + b l 3)}^{2}} + 4} - (a 1 b 2 - b 1 a 2) (- 2 (1 + \sqrt{{a l 1}^{2} + 6 a l 1 b l 1 + {b l 1}^{2}}) \sqrt{({a l 3}^{2} + 6 a l 3 b l 3 + {b l 3}^{2}) {(- 2 + a l 1 + a l 2 + a l 3 + b l 1 + b l 2 + b l 3)}^{2}} - {({a l 1}^{2} + 6 a l 1 b l 1 + {b l 1}^{2})}^{\frac{3}{2}} + ({a l 1}^{2} + 6 a l 1 b l 1 - 2 {a l 3}^{2} - 12 a l 3 b l 3 + {b l 1}^{2} - 2 {b l 3}^{2}) \sqrt{{a l 1}^{2} + 6 a l 1 b l 1 + {b l 1}^{2}} - 2 {b l 3}^{2} - 12 a l 3 b l 3 - 2 {a l 3}^{2}) b 3) \frac{1}{\sqrt{{a l 1}^{2} + (2 a l 2 + 2 a l 3 + 2 b l 1 + 2 b l 2 + 2 b l 3 - 4) a l 1 + {a l 2}^{2} + (2 a l 3 + 2 b l 1 + 2 b l 2 + 2 b l 3 - 4) a l 2 + 2 {a l 3}^{2} + (2 b l 1 + 2 b l 2 + 8 b l 3 - 4) a l 3 + {b l 1}^{2} + (2 b l 2 + 2 b l 3 - 4) b l 1 + {b l 2}^{2} + (2 b l 3 - 4) b l 2 + 2 {b l 3}^{2} - 4 b l 3 + 2 \sqrt{({a l 3}^{2} + 6 a l 3 b l 3 + {b l 3}^{2}) {(- 2 + a l 1 + a l 2 + a l 3 + b l 1 + b l 2 + b l 3)}^{2}} + 4}}, \frac{1}{2} \sqrt{{a l 1}^{2} + 6 a l 1 b l 1 + {b l 1}^{2}} + \frac{1}{2} \sqrt{{a l 2}^{2} + 6 a l 2 b l 2 + {b l 2}^{2}} + 1 + \frac{1}{2} \sqrt{{a l 1}^{2} + (2 a l 2 + 2 a l 3 + 2 b l 1 + 2 b l 2 + 2 b l 3 - 4) a l 1 + {a l 2}^{2} + (2 a l 3 + 2 b l 1 + 2 b l 2 + 2 b l 3 - 4) a l 2 + 2 {a l 3}^{2} + (2 b l 1 + 2 b l 2 + 8 b l 3 - 4) a l 3 + {b l 1}^{2} + (2 b l 2 + 2 b l 3 - 4) b l 1 + {b l 2}^{2} + (2 b l 3 - 4) b l 2 + 2 {b l 3}^{2} - 4 b l 3 + 2 \sqrt{({a l 3}^{2} + 6 a l 3 b l 3 + {b l 3}^{2}) {(- 2 + a l 1 + a l 2 + a l 3 + b l 1 + b l 2 + b l 3)}^{2}} + 4}, \frac{1}{2} ((\sqrt{{a l 1}^{2} + 6 a l 1 b l 1 + {b l 1}^{2}} + \sqrt{{a l 2}^{2} + 6 a l 2 b l 2 + {b l 2}^{2}} + 2) \sqrt{{a l 1}^{2} + (2 a l 2 + 2 a l 3 + 2 b l 1 + 2 b l 2 + 2 b l 3 - 4) a l 1 + {a l 2}^{2} + (2 a l 3 + 2 b l 1 + 2 b l 2 + 2 b l 3 - 4) a l 2 + 2 {a l 3}^{2} + (2 b l 1 + 2 b l 2 + 8 b l 3 - 4) a l 3 + {b l 1}^{2} + (2 b l 2 + 2 b l 3 - 4) b l 1 + {b l 2}^{2} + (2 b l 3 - 4) b l 2 + 2 {b l 3}^{2} - 4 b l 3 + 2 \sqrt{({a l 3}^{2} + 6 a l 3 b l 3 + {b l 3}^{2}) {(- 2 + a l 1 + a l 2 + a l 3 + b l 1 + b l 2 + b l 3)}^{2}} + 4} - (2 a l 1 + 2 a l 2 - 4 a l 3 + 2 b l 1 + 2 b l 2 - 4) b l 3 - (a l 1 + a l 2 + b l 1 + b l 2 - 2) (a l 1 + a l 2 + 2 a l 3 + b l 1 + b l 2 - 2)) \frac{1}{\sqrt{{a l 1}^{2} + (2 a l 2 + 2 a l 3 + 2 b l 1 + 2 b l 2 + 2 b l 3 - 4) a l 1 + {a l 2}^{2} + (2 a l 3 + 2 b l 1 + 2 b l 2 + 2 b l 3 - 4) a l 2 + 2 {a l 3}^{2} + (2 b l 1 + 2 b l 2 + 8 b l 3 - 4) a l 3 + {b l 1}^{2} + (2 b l 2 + 2 b l 3 - 4) b l 1 + {b l 2}^{2} + (2 b l 3 - 4) b l 2 + 2 {b l 3}^{2} - 4 b l 3 + 2 \sqrt{({a l 3}^{2} + 6 a l 3 b l 3 + {b l 3}^{2}) {(- 2 + a l 1 + a l 2 + a l 3 + b l 1 + b l 2 + b l 3)}^{2}} + 4}}, 1 + \sqrt{{a l 1}^{2} + 6 a l 1 b l 1 + {b l 1}^{2}}, 1 + \sqrt{{a l 2}^{2} + 6 a l 2 b l 2 + {b l 2}^{2}}, \frac{b 2 (- b 1 x + a 1)}{a 1 b 2 - b 1 a 2}) {(b 1 x - a 1)}^{\frac{a l 1}{2} + \frac{b l 1}{2} + \frac{1}{2} \sqrt{{a l 1}^{2} + 6 a l 1 b l 1 + {b l 1}^{2}}} {(b 2 x - a 2)}^{\frac{a l 2}{2} + \frac{b l 2}{2} + \frac{1}{2} \sqrt{{a l 2}^{2} + 6 a l 2 b l 2 + {b l 2}^{2}}} {(b 3 x - a 3)}^{\frac{1}{2} ((a l 3 + b l 3) \sqrt{(2 a l 1 + 2 a l 2 + 2 a l 3 + 2 b l 1 + 2 b l 2 + 2 b l 3 - 4) \sqrt{{a l 3}^{2} + 6 a l 3 b l 3 + {b l 3}^{2}} + 2 {b l 3}^{2} + (2 a l 1 + 2 a l 2 + 8 a l 3 + 2 b l 1 + 2 b l 2 - 4) b l 3 + {b l 2}^{2} + (2 a l 1 + 2 a l 2 + 2 a l 3 + 2 b l 1 - 4) b l 2 + {b l 1}^{2} + (2 a l 1 + 2 a l 2 + 2 a l 3 - 4) b l 1 + 2 {a l 3}^{2} + (2 a l 1 + 2 a l 2 - 4) a l 3 + {(a l 1 + a l 2 - 2)}^{2}} + (- 2 + a l 1 + a l 2 + a l 3 + b l 1 + b l 2 + b l 3) \sqrt{{a l 3}^{2} + 6 a l 3 b l 3 + {b l 3}^{2}} + {a l 3}^{2} + 6 a l 3 b l 3 + {b l 3}^{2}) \frac{1}{\sqrt{(2 a l 1 + 2 a l 2 + 2 a l 3 + 2 b l 1 + 2 b l 2 + 2 b l 3 - 4) \sqrt{{a l 3}^{2} + 6 a l 3 b l 3 + {b l 3}^{2}} + 2 {b l 3}^{2} + (2 a l 1 + 2 a l 2 + 8 a l 3 + 2 b l 1 + 2 b l 2 - 4) b l 3 + {b l 2}^{2} + (2 a l 1 + 2 a l 2 + 2 a l 3 + 2 b l 1 - 4) b l 2 + {b l 1}^{2} + (2 a l 1 + 2 a l 2 + 2 a l 3 - 4) b l 1 + 2 {a l 3}^{2} + (2 a l 1 + 2 a l 2 - 4) a l 3 + {(a l 1 + a l 2 - 2)}^{2}}}}}$

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