ODE No. 1188

2.1188 ODE No. 1188

Problem in Latex
Mathematica input
Maple input

$(a x + b) y^{'} (x) + c y (x) + x^{2} y^{″} (x) = 0$ ✓ Mathematica : cpu = 0.155804 (sec), leaf count = 266

${{y (x) \to c_{1} i^{- \sqrt{a^{2} - 2 a - 4 c + 1} + a - 1} b^{\frac{1}{2} (- \sqrt{a^{2} - 2 a - 4 c + 1} + a - 1)} {(\frac{1}{x})}^{\frac{1}{2} (- \sqrt{a^{2} - 2 a - 4 c + 1} + a - 1)}_{1} F_{1} (\frac{a}{2} - \frac{1}{2} \sqrt{a^{2} - 2 a - 4 c + 1} - \frac{1}{2}; 1 - \sqrt{a^{2} - 2 a - 4 c + 1}; \frac{b}{x}) + c_{2} i^{\sqrt{a^{2} - 2 a - 4 c + 1} + a - 1} b^{\frac{1}{2} (\sqrt{a^{2} - 2 a - 4 c + 1} + a - 1)} {(\frac{1}{x})}^{\frac{1}{2} (\sqrt{a^{2} - 2 a - 4 c + 1} + a - 1)}_{1} F_{1} (\frac{a}{2} + \frac{1}{2} \sqrt{a^{2} - 2 a - 4 c + 1} - \frac{1}{2}; \sqrt{a^{2} - 2 a - 4 c + 1} + 1; \frac{b}{x})}}$ ✓ Maple : cpu = 0.47 (sec), leaf count = 114

${y (x) = x^{- \frac{1}{2} \sqrt{a^{2} - 2 a - 4 c + 1} - \frac{a}{2} + \frac{1}{2}} (M (- \frac{1}{2} + \frac{1}{2} \sqrt{a^{2} - 2 a - 4 c + 1} + \frac{a}{2}, 1 + \sqrt{a^{2} - 2 a - 4 c + 1}, \frac{b}{x})_C 1 + U (- \frac{1}{2} + \frac{1}{2} \sqrt{a^{2} - 2 a - 4 c + 1} + \frac{a}{2}, 1 + \sqrt{a^{2} - 2 a - 4 c + 1}, \frac{b}{x})_C 2)}$

[next] [prev] [prev-tail] [front] [up]