ODE No. 1298

2.1298 ODE No. 1298

Problem in Latex
Mathematica input
Maple input

$(a x^{2} + 1) y^{″} (x) + b x y^{'} (x) + c y (x) = 0$ ✓ Mathematica : cpu = 0.0771942 (sec), leaf count = 162

${{y (x) \to c_{1} {(a x^{2} + 1)}^{\frac{2 a - b}{4 a}} P_{\frac{\sqrt{a^{2} - 2 b a - 4 c a + b^{2}} - a}{2 a}}^{\frac{b - 2 a}{2 a}} (i \sqrt{a} x) + c_{2} {(a x^{2} + 1)}^{\frac{2 a - b}{4 a}} Q_{\frac{\sqrt{a^{2} - 2 b a - 4 c a + b^{2}} - a}{2 a}}^{\frac{b - 2 a}{2 a}} (i \sqrt{a} x)}}$

✓ Maple : cpu = 0.184 (sec), leaf count = 143

${y (x) =_C 1 {(a x^{2} + 1)}^{\frac{2 a - b}{4 a}} L e g e n d r e P (\frac{1}{2 a} (\sqrt{a^{2} + (- 2 b - 4 c) a + b^{2}} - a), \frac{2 a - b}{2 a}, \sqrt{- a} x) +_C 2 {(a x^{2} + 1)}^{\frac{2 a - b}{4 a}} L e g e n d r e Q (\frac{1}{2 a} (\sqrt{a^{2} + (- 2 b - 4 c) a + b^{2}} - a), \frac{2 a - b}{2 a}, \sqrt{- a} x)}$

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