ODE No. 417

3.417 ODE No. 417

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

Mathematica: cpu = 0.374047 (sec), leaf count = 430 ${{y (x) \to - \frac{8 a^{2}}{4 a - \sinh (c_{1}) - \cosh (c_{1})} - \frac{\sqrt{16 a^{3} \sinh (c_{1}) + 16 a^{3} \cosh (c_{1}) - 8 a^{2} x \sinh (c_{1}) - 8 a^{2} x \cosh (c_{1}) - 8 a^{2} \sinh (2 c_{1}) - 8 a^{2} \cosh (2 c_{1}) + a x^{2} \sinh (c_{1}) + a x^{2} \cosh (c_{1}) + 2 a x \sinh (2 c_{1}) + 2 a x \cosh (2 c_{1}) + a \sinh (3 c_{1}) + a \cosh (3 c_{1})}}{4 a - \sinh (c_{1}) - \cosh (c_{1})} - \frac{2 a x}{4 a - \sinh (c_{1}) - \cosh (c_{1})} + \frac{2 a \sinh (c_{1})}{4 a - \sinh (c_{1}) - \cosh (c_{1})} + \frac{2 a \cosh (c_{1})}{4 a - \sinh (c_{1}) - \cosh (c_{1})}}, {y (x) \to - \frac{8 a^{2}}{4 a - \sinh (c_{1}) - \cosh (c_{1})} + \frac{\sqrt{16 a^{3} \sinh (c_{1}) + 16 a^{3} \cosh (c_{1}) - 8 a^{2} x \sinh (c_{1}) - 8 a^{2} x \cosh (c_{1}) - 8 a^{2} \sinh (2 c_{1}) - 8 a^{2} \cosh (2 c_{1}) + a x^{2} \sinh (c_{1}) + a x^{2} \cosh (c_{1}) + 2 a x \sinh (2 c_{1}) + 2 a x \cosh (2 c_{1}) + a \sinh (3 c_{1}) + a \cosh (3 c_{1})}}{4 a - \sinh (c_{1}) - \cosh (c_{1})} - \frac{2 a x}{4 a - \sinh (c_{1}) - \cosh (c_{1})} + \frac{2 a \sinh (c_{1})}{4 a - \sinh (c_{1}) - \cosh (c_{1})} + \frac{2 a \cosh (c_{1})}{4 a - \sinh (c_{1}) - \cosh (c_{1})}}}$

Maple: cpu = 0.484 (sec), leaf count = 33 ${y (x) = - 2 \sqrt{a x}, y (x) = 2 \sqrt{a x}, y (x) =_C 1 x + \frac{a}{_C 1}}$

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