ODE No. 1143

4.143 ODE No. 1143

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

Problem in Latex
Mathematica input
Maple input

Mathematica: cpu = 0.045006 (sec), leaf count = 93 ${{y (x) \to c_{1} e^{\frac{a \log (x) - b x}{2 a}} U (- \frac{c - b}{b}, \frac{3}{2}, \frac{b x}{2 a}) + c_{2} e^{\frac{a \log (x) - b x}{2 a}} L_{\frac{c - b}{b}}^{\frac{1}{2}} (\frac{b x}{2 a})}}$

Maple: cpu = 0.078 (sec), leaf count = 67 ${y (x) =_C 1 e^{- \frac{b x}{2 a}} M (\frac{b - c}{b}, \frac{3}{2}, \frac{b x}{2 a}) \sqrt{x} +_C 2 e^{- \frac{b x}{2 a}} U (\frac{b - c}{b}, \frac{3}{2}, \frac{b x}{2 a}) \sqrt{x}}$

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