ODE No. 1392

4.392 ODE No. 1392

$\frac{d^{2}}{d x^{2}} y (x) = - \frac{b x \frac{d}{d x} y (x)}{(x^{2} - 1) a} - \frac{(c x^{2} + d x + e) y (x)}{a {(x^{2} - 1)}^{2}} = 0$

Mathematica: cpu = 83.233069 (sec), leaf count = 1763961

Result too large for latex to process

Maple: cpu = 0.157 (sec), leaf count = 613 ${y (x) =_C 1 {(- \frac{1}{2} + \frac{x}{2})}^{\frac{1}{4 a} (2 a + \sqrt{4 a^{2} + (- 4 b - 4 c - 4 d - 4 e) a + b^{2}})} {(x^{2} - 1)}^{- \frac{b}{4 a}}_{2} F_{1} (\frac{1}{4 a} (\sqrt{4 a^{2} + (- 4 b - 4 c - 4 d - 4 e) a + b^{2}} + 2 \sqrt{a^{2} + (- 2 b - 4 c) a + b^{2}} - \sqrt{4 a^{2} + (- 4 b - 4 c + 4 d - 4 e) a + b^{2}} + 2 a), - \frac{1}{4 a} (- \sqrt{4 a^{2} + (- 4 b - 4 c - 4 d - 4 e) a + b^{2}} + 2 \sqrt{a^{2} + (- 2 b - 4 c) a + b^{2}} + \sqrt{4 a^{2} + (- 4 b - 4 c + 4 d - 4 e) a + b^{2}} - 2 a); - \frac{1}{2 a} (- 2 a + \sqrt{4 a^{2} + (- 4 b - 4 c + 4 d - 4 e) a + b^{2}}); \frac{1}{2} + \frac{x}{2}) {(\frac{1}{2} + \frac{x}{2})}^{\frac{1}{4 a} (2 a - \sqrt{4 a^{2} + (- 4 b - 4 c + 4 d - 4 e) a + b^{2}})} +_C 2 {(- \frac{1}{2} + \frac{x}{2})}^{\frac{1}{4 a} (2 a + \sqrt{4 a^{2} + (- 4 b - 4 c - 4 d - 4 e) a + b^{2}})} {(x^{2} - 1)}^{- \frac{b}{4 a}}_{2} F_{1} (\frac{1}{4 a} (\sqrt{4 a^{2} + (- 4 b - 4 c - 4 d - 4 e) a + b^{2}} - 2 \sqrt{a^{2} + (- 2 b - 4 c) a + b^{2}} + \sqrt{4 a^{2} + (- 4 b - 4 c + 4 d - 4 e) a + b^{2}} + 2 a), \frac{1}{4 a} (\sqrt{4 a^{2} + (- 4 b - 4 c - 4 d - 4 e) a + b^{2}} + 2 \sqrt{a^{2} + (- 2 b - 4 c) a + b^{2}} + \sqrt{4 a^{2} + (- 4 b - 4 c + 4 d - 4 e) a + b^{2}} + 2 a); \frac{1}{2 a} (2 a + \sqrt{4 a^{2} + (- 4 b - 4 c + 4 d - 4 e) a + b^{2}}); \frac{1}{2} + \frac{x}{2}) {(\frac{1}{2} + \frac{x}{2})}^{\frac{1}{4 a} (2 a + \sqrt{4 a^{2} + (- 4 b - 4 c + 4 d - 4 e) a + b^{2}})}}$

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