ODE No. 164

3.164 ODE No. 164

$2 x^{2} \frac{d}{d x} y (x) - 2 {(y (x))}^{2} - 3 x y (x) + 2 a^{2} x = 0$

Problem in Latex
Mathematica input
Maple input

Mathematica: cpu = 0.082010 (sec), leaf count = 131 ${{y (x) \to - \frac{x^{2} (c_{1} (\frac{a e^{- \frac{2 a}{\sqrt{x}}}}{x} + \frac{e^{- \frac{2 a}{\sqrt{x}}}}{2 \sqrt{x}}) - \frac{e^{\frac{2 a}{\sqrt{x}}}}{4 a \sqrt{x}} + \frac{e^{\frac{2 a}{\sqrt{x}}}}{2 x})}{c_{1} \sqrt{x} e^{- \frac{2 a}{\sqrt{x}}} - \frac{\sqrt{x} e^{\frac{2 a}{\sqrt{x}}}}{2 a}}}}$

Maple: cpu = 0.156 (sec), leaf count = 102 ${y (x) = 1 ((- 2 x_C 1 \sqrt{- \frac{a^{2}}{x}} - x) \sin (2 \sqrt{- \frac{a^{2}}{x}}) - x (_C 1 - 2 \sqrt{- \frac{a^{2}}{x}}) \cos (2 \sqrt{- \frac{a^{2}}{x}})) {(2 \cos (2 \sqrt{- \frac{a^{2}}{x}})_C 1 + 2 \sin (2 \sqrt{- \frac{a^{2}}{x}}))}^{- 1}}$

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