ODE No. 507

3.507 ODE No. 507

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

Mathematica: cpu = 29.710773 (sec), leaf count = 443 ${Solve [{x = \frac{a^{2} K $ 1432838 y (K $ 1432838) - \sqrt{a^{2} {K $ 1432838}^{2} ({K $ 1432838}^{2} + 1) y (K $ 1432838)^{4}}}{a^{2} {K $ 1432838}^{2}}, y (x) = \frac{1}{4} (- \frac{a c_{1} \sqrt{K $ 1432838}}{\sqrt[4]{{K $ 1432838}^{2} + 1}} - \frac{2 a \sqrt[4]{\frac{{K $ 1432838}^{2} + 1}{{K $ 1432838}^{2}}}_{2} F_{1} (\frac{1}{4}, \frac{1}{2}; \frac{3}{2}; - \frac{1}{{K $ 1432838}^{2}})}{\sqrt{{K $ 1432838}^{2} + 1}})}, {y (x), K $ 1432838}], Solve [{x = \frac{a^{2} K $ 1432838 y (K $ 1432838) - \sqrt{a^{2} {K $ 1432838}^{2} ({K $ 1432838}^{2} + 1) y (K $ 1432838)^{4}}}{a^{2} {K $ 1432838}^{2}}, y (x) = \frac{1}{4} (\frac{2 a \sqrt[4]{\frac{{K $ 1432838}^{2} + 1}{{K $ 1432838}^{2}}}_{2} F_{1} (\frac{1}{4}, \frac{1}{2}; \frac{3}{2}; - \frac{1}{{K $ 1432838}^{2}})}{\sqrt{{K $ 1432838}^{2} + 1}} - \frac{a c_{1} \sqrt{K $ 1432838}}{\sqrt[4]{{K $ 1432838}^{2} + 1}})}, {y (x), K $ 1432838}], Solve [{x = \frac{\sqrt{a^{2} {K $ 1435339}^{2} ({K $ 1435339}^{2} + 1) y (K $ 1435339)^{4}} + a^{2} K $ 1435339 y (K $ 1435339)}{a^{2} {K $ 1435339}^{2}}, y (x) = \frac{1}{4} (\frac{a c_{1} \sqrt{K $ 1435339}}{\sqrt[4]{{K $ 1435339}^{2} + 1}} - \frac{2 a \sqrt[4]{\frac{{K $ 1435339}^{2} + 1}{{K $ 1435339}^{2}}}_{2} F_{1} (\frac{1}{4}, \frac{1}{2}; \frac{3}{2}; - \frac{1}{{K $ 1435339}^{2}})}{\sqrt{{K $ 1435339}^{2} + 1}})}, {y (x), K $ 1435339}], Solve [{x = \frac{\sqrt{a^{2} {K $ 1435339}^{2} ({K $ 1435339}^{2} + 1) y (K $ 1435339)^{4}} + a^{2} K $ 1435339 y (K $ 1435339)}{a^{2} {K $ 1435339}^{2}}, y (x) = \frac{1}{4} (\frac{a c_{1} \sqrt{K $ 1435339}}{\sqrt[4]{{K $ 1435339}^{2} + 1}} + \frac{2 a \sqrt[4]{\frac{{K $ 1435339}^{2} + 1}{{K $ 1435339}^{2}}}_{2} F_{1} (\frac{1}{4}, \frac{1}{2}; \frac{3}{2}; - \frac{1}{{K $ 1435339}^{2}})}{\sqrt{{K $ 1435339}^{2} + 1}})}, {y (x), K $ 1435339}]}$

Maple: cpu = 0 (sec), leaf count = 0 $hanged$

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