ODE No. 475

3.475 ODE No. 475

$4 y (x) {(\frac{d}{d x} y (x))}^{2} + 2 x \frac{d}{d x} y (x) - y (x) = 0$

Mathematica: cpu = 0.097512 (sec), leaf count = 205 ${{y (x) \to - \frac{1}{2} e^{2 c_{1}} \sqrt{e^{4 c_{1}} - 2 x}}, {y (x) \to \frac{1}{2} e^{2 c_{1}} \sqrt{e^{4 c_{1}} - 2 x}}, {y (x) \to - \frac{1}{2} (\sinh (2 c_{1}) + \cosh (2 c_{1})) \sqrt{\sinh (4 c_{1}) + \cosh (4 c_{1}) - 2 x}}, {y (x) \to \frac{1}{2} (\sinh (2 c_{1}) + \cosh (2 c_{1})) \sqrt{\sinh (4 c_{1}) + \cosh (4 c_{1}) - 2 x}}, {y (x) \to - \frac{1}{2} (\sinh (2 c_{1}) + \cosh (2 c_{1})) \sqrt{\sinh (4 c_{1}) + \cosh (4 c_{1}) + 2 x}}, {y (x) \to \frac{1}{2} (\sinh (2 c_{1}) + \cosh (2 c_{1})) \sqrt{\sinh (4 c_{1}) + \cosh (4 c_{1}) + 2 x}}}$

Maple: cpu = 0.936 (sec), leaf count = 69 ${y (x) = \sqrt{{_C 1}^{2} -_C 1 x}, y (x) = \sqrt{{_C 1}^{2} +_C 1 x}, y (x) = - \frac{i}{2} x, y (x) = \frac{i}{2} x, y (x) = - \sqrt{{_C 1}^{2} -_C 1 x}, y (x) = - \sqrt{{_C 1}^{2} +_C 1 x}}$

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