ODE No. 420

3.420 ODE No. 420

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

Mathematica: cpu = 1.329169 (sec), leaf count = 11757 ${{y (x) \to - \sqrt{\frac{9 a^{4} (\cosh (3 c_{1}) - \sinh (3 c_{1})) x^{8}}{16 \sqrt[3]{27 a^{6} x^{12} - 144 a^{5} \cosh (3 c_{1}) x^{9} - 144 a^{5} \sinh (3 c_{1}) x^{9} + 272 a^{4} \cosh (6 c_{1}) x^{6} + 272 a^{4} \sinh (6 c_{1}) x^{6} - 256 a^{3} \cosh (9 c_{1}) x^{3} - 256 a^{3} \sinh (9 c_{1}) x^{3} + 128 a^{2} \cosh (12 c_{1}) + 128 a^{2} \sinh (12 c_{1}) + 64 \sqrt{- a^{9} \cosh (9 c_{1}) x^{15} - a^{9} \sinh (9 c_{1}) x^{15} + 7 a^{8} \cosh (12 c_{1}) x^{12} + 7 a^{8} \sinh (12 c_{1}) x^{12} - 19 a^{7} \cosh (15 c_{1}) x^{9} - 19 a^{7} \sinh (15 c_{1}) x^{9} + 25 a^{6} \cosh (18 c_{1}) x^{6} + 25 a^{6} \sinh (18 c_{1}) x^{6} - 16 a^{5} \cosh (21 c_{1}) x^{3} - 16 a^{5} \sinh (21 c_{1}) x^{3} + 4 a^{4} \cosh (24 c_{1}) + 4 a^{4} \sinh (24 c_{1})}}} - \frac{2 a^{3} x^{5}}{\sqrt[3]{27 a^{6} x^{12} - 144 a^{5} \cosh (3 c_{1}) x^{9} - 144 a^{5} \sinh (3 c_{1}) x^{9} + 272 a^{4} \cosh (6 c_{1}) x^{6} + 272 a^{4} \sinh (6 c_{1}) x^{6} - 256 a^{3} \cosh (9 c_{1}) x^{3} - 256 a^{3} \sinh (9 c_{1}) x^{3} + 128 a^{2} \cosh (12 c_{1}) + 128 a^{2} \sinh (12 c_{1}) + 64 \sqrt{- a^{9} \cosh (9 c_{1}) x^{15} - a^{9} \sinh (9 c_{1}) x^{15} + 7 a^{8} \cosh (12 c_{1}) x^{12} + 7 a^{8} \sinh (12 c_{1}) x^{12} - 19 a^{7} \cosh (15 c_{1}) x^{9} - 19 a^{7} \sinh (15 c_{1}) x^{9} + 25 a^{6} \cosh (18 c_{1}) x^{6} + 25 a^{6} \sinh (18 c_{1}) x^{6} - 16 a^{5} \cosh (21 c_{1}) x^{3} - 16 a^{5} \sinh (21 c_{1}) x^{3} + 4 a^{4} \cosh (24 c_{1}) + 4 a^{4} \sinh (24 c_{1})}}} + \frac{3}{16} a^{2} \cosh (3 c_{1}) x^{4} - \frac{3}{16} a^{2} \sinh (3 c_{1}) x^{4} + \frac{2 a^{2} (\cosh (3 c_{1}) + \sinh (3 c_{1})) x^{2}}{\sqrt[3]{27 a^{6} x^{12} - 144 a^{5} \cosh (3 c_{1}) x^{9} - 144 a^{5} \sinh (3 c_{1}) x^{9} + 272 a^{4} \cosh (6 c_{1}) x^{6} + 272 a^{4} \sinh (6 c_{1}) x^{6} - 256 a^{3} \cosh (9 c_{1}) x^{3} - 256 a^{3} \sinh (9 c_{1}) x^{3} + 128 a^{2} \cosh (12 c_{1}) + 128 a^{2} \sinh (12 c_{1}) + 64 \sqrt{- a^{9} \cosh (9 c_{1}) x^{15} - a^{9} \sinh (9 c_{1}) x^{15} + 7 a^{8} \cosh (12 c_{1}) x^{12} + 7 a^{8} \sinh (12 c_{1}) x^{12} - 19 a^{7} \cosh (15 c_{1}) x^{9} - 19 a^{7} \sinh (15 c_{1}) x^{9} + 25 a^{6} \cosh (18 c_{1}) x^{6} + 25 a^{6} \sinh (18 c_{1}) x^{6} - 16 a^{5} \cosh (21 c_{1}) x^{3} - 16 a^{5} \sinh (21 c_{1}) x^{3} + 4 a^{4} \cosh (24 c_{1}) + 4 a^{4} \sinh (24 c_{1})}}} + a x + \frac{1}{16} (\cosh (3 c_{1}) - \sinh (3 c_{1})) \sqrt[3]{27 a^{6} x^{12} - 144 a^{5} \cosh (3 c_{1}) x^{9} - 144 a^{5} \sinh (3 c_{1}) x^{9} + 272 a^{4} \cosh (6 c_{1}) x^{6} + 272 a^{4} \sinh (6 c_{1}) x^{6} - 256 a^{3} \cosh (9 c_{1}) x^{3} - 256 a^{3} \sinh (9 c_{1}) x^{3} + 128 a^{2} \cosh (12 c_{1}) + 128 a^{2} \sinh (12 c_{1}) + 64 \sqrt{- a^{9} \cosh (9 c_{1}) x^{15} - a^{9} \sinh (9 c_{1}) x^{15} + 7 a^{8} \cosh (12 c_{1}) x^{12} + 7 a^{8} \sinh (12 c_{1}) x^{12} - 19 a^{7} \cosh (15 c_{1}) x^{9} - 19 a^{7} \sinh (15 c_{1}) x^{9} + 25 a^{6} \cosh (18 c_{1}) x^{6} + 25 a^{6} \sinh (18 c_{1}) x^{6} - 16 a^{5} \cosh (21 c_{1}) x^{3} - 16 a^{5} \sinh (21 c_{1}) x^{3} + 4 a^{4} \cosh (24 c_{1}) + 4 a^{4} \sinh (24 c_{1})}}}}, {y (x) \to \sqrt{\frac{9 a^{4} (\cosh (3 c_{1}) - \sinh (3 c_{1})) x^{8}}{16 \sqrt[3]{27 a^{6} x^{12} - 144 a^{5} \cosh (3 c_{1}) x^{9} - 144 a^{5} \sinh (3 c_{1}) x^{9} + 272 a^{4} \cosh (6 c_{1}) x^{6} + 272 a^{4} \sinh (6 c_{1}) x^{6} - 256 a^{3} \cosh (9 c_{1}) x^{3} - 256 a^{3} \sinh (9 c_{1}) x^{3} + 128 a^{2} \cosh (12 c_{1}) + 128 a^{2} \sinh (12 c_{1}) + 64 \sqrt{- a^{9} \cosh (9 c_{1}) x^{15} - a^{9} \sinh (9 c_{1}) x^{15} + 7 a^{8} \cosh (12 c_{1}) x^{12} + 7 a^{8} \sinh (12 c_{1}) x^{12} - 19 a^{7} \cosh (15 c_{1}) x^{9} - 19 a^{7} \sinh (15 c_{1}) x^{9} + 25 a^{6} \cosh (18 c_{1}) x^{6} + 25 a^{6} \sinh (18 c_{1}) x^{6} - 16 a^{5} \cosh (21 c_{1}) x^{3} - 16 a^{5} \sinh (21 c_{1}) x^{3} + 4 a^{4} \cosh (24 c_{1}) + 4 a^{4} \sinh (24 c_{1})}}} - \frac{2 a^{3} x^{5}}{\sqrt[3]{27 a^{6} x^{12} - 144 a^{5} \cosh (3 c_{1}) x^{9} - 144 a^{5} \sinh (3 c_{1}) x^{9} + 272 a^{4} \cosh (6 c_{1}) x^{6} + 272 a^{4} \sinh (6 c_{1}) x^{6} - 256 a^{3} \cosh (9 c_{1}) x^{3} - 256 a^{3} \sinh (9 c_{1}) x^{3} + 128 a^{2} \cosh (12 c_{1}) + 128 a^{2} \sinh (12 c_{1}) + 64 \sqrt{- a^{9} \cosh (9 c_{1}) x^{15} - a^{9} \sinh (9 c_{1}) x^{15} + 7 a^{8} \cosh (12 c_{1}) x^{12} + 7 a^{8} \sinh (12 c_{1}) x^{12} - 19 a^{7} \cosh (15 c_{1}) x^{9} - 19 a^{7} \sinh (15 c_{1}) x^{9} + 25 a^{6} \cosh (18 c_{1}) x^{6} + 25 a^{6} \sinh (18 c_{1}) x^{6} - 16 a^{5} \cosh (21 c_{1}) x^{3} - 16 a^{5} \sinh (21 c_{1}) x^{3} + 4 a^{4} \cosh (24 c_{1}) + 4 a^{4} \sinh (24 c_{1})}}} + \frac{3}{16} a^{2} \cosh (3 c_{1}) x^{4} - \frac{3}{16} a^{2} \sinh (3 c_{1}) x^{4} + \frac{2 a^{2} (\cosh (3 c_{1}) + \sinh (3 c_{1})) x^{2}}{\sqrt[3]{27 a^{6} x^{12} - 144 a^{5} \cosh (3 c_{1}) x^{9} - 144 a^{5} \sinh (3 c_{1}) x^{9} + 272 a^{4} \cosh (6 c_{1}) x^{6} + 272 a^{4} \sinh (6 c_{1}) x^{6} - 256 a^{3} \cosh (9 c_{1}) x^{3} - 256 a^{3} \sinh (9 c_{1}) x^{3} + 128 a^{2} \cosh (12 c_{1}) + 128 a^{2} \sinh (12 c_{1}) + 64 \sqrt{- a^{9} \cosh (9 c_{1}) x^{15} - a^{9} \sinh (9 c_{1}) x^{15} + 7 a^{8} \cosh (12 c_{1}) x^{12} + 7 a^{8} \sinh (12 c_{1}) x^{12} - 19 a^{7} \cosh (15 c_{1}) x^{9} - 19 a^{7} \sinh (15 c_{1}) x^{9} + 25 a^{6} \cosh (18 c_{1}) x^{6} + 25 a^{6} \sinh (18 c_{1}) x^{6} - 16 a^{5} \cosh (21 c_{1}) x^{3} - 16 a^{5} \sinh (21 c_{1}) x^{3} + 4 a^{4} \cosh (24 c_{1}) + 4 a^{4} \sinh (24 c_{1})}}} + a x + \frac{1}{16} (\cosh (3 c_{1}) - \sinh (3 c_{1})) \sqrt[3]{27 a^{6} x^{12} - 144 a^{5} \cosh (3 c_{1}) x^{9} - 144 a^{5} \sinh (3 c_{1}) x^{9} + 272 a^{4} \cosh (6 c_{1}) x^{6} + 272 a^{4} \sinh (6 c_{1}) x^{6} - 256 a^{3} \cosh (9 c_{1}) x^{3} - 256 a^{3} \sinh (9 c_{1}) x^{3} + 128 a^{2} \cosh (12 c_{1}) + 128 a^{2} \sinh (12 c_{1}) + 64 \sqrt{- a^{9} \cosh (9 c_{1}) x^{15} - a^{9} \sinh (9 c_{1}) x^{15} + 7 a^{8} \cosh (12 c_{1}) x^{12} + 7 a^{8} \sinh (12 c_{1}) x^{12} - 19 a^{7} \cosh (15 c_{1}) x^{9} - 19 a^{7} \sinh (15 c_{1}) x^{9} + 25 a^{6} \cosh (18 c_{1}) x^{6} + 25 a^{6} \sinh (18 c_{1}) x^{6} - 16 a^{5} \cosh (21 c_{1}) x^{3} - 16 a^{5} \sinh (21 c_{1}) x^{3} + 4 a^{4} \cosh (24 c_{1}) + 4 a^{4} \sinh (24 c_{1})}}}}, {y (x) \to - \sqrt{\frac{9 i \sqrt{3} a^{4} (\cosh (3 c_{1}) - \sinh (3 c_{1})) x^{8}}{32 \sqrt[3]{27 a^{6} x^{12} - 144 a^{5} \cosh (3 c_{1}) x^{9} - 144 a^{5} \sinh (3 c_{1}) x^{9} + 272 a^{4} \cosh (6 c_{1}) x^{6} + 272 a^{4} \sinh (6 c_{1}) x^{6} - 256 a^{3} \cosh (9 c_{1}) x^{3} - 256 a^{3} \sinh (9 c_{1}) x^{3} + 128 a^{2} \cosh (12 c_{1}) + 128 a^{2} \sinh (12 c_{1}) + 64 \sqrt{- a^{9} \cosh (9 c_{1}) x^{15} - a^{9} \sinh (9 c_{1}) x^{15} + 7 a^{8} \cosh (12 c_{1}) x^{12} + 7 a^{8} \sinh (12 c_{1}) x^{12} - 19 a^{7} \cosh (15 c_{1}) x^{9} - 19 a^{7} \sinh (15 c_{1}) x^{9} + 25 a^{6} \cosh (18 c_{1}) x^{6} + 25 a^{6} \sinh (18 c_{1}) x^{6} - 16 a^{5} \cosh (21 c_{1}) x^{3} - 16 a^{5} \sinh (21 c_{1}) x^{3} + 4 a^{4} \cosh (24 c_{1}) + 4 a^{4} \sinh (24 c_{1})}}} - \frac{9 a^{4} (\cosh (3 c_{1}) - \sinh (3 c_{1})) x^{8}}{32 \sqrt[3]{27 a^{6} x^{12} - 144 a^{5} \cosh (3 c_{1}) x^{9} - 144 a^{5} \sinh (3 c_{1}) x^{9} + 272 a^{4} \cosh (6 c_{1}) x^{6} + 272 a^{4} \sinh (6 c_{1}) x^{6} - 256 a^{3} \cosh (9 c_{1}) x^{3} - 256 a^{3} \sinh (9 c_{1}) x^{3} + 128 a^{2} \cosh (12 c_{1}) + 128 a^{2} \sinh (12 c_{1}) + 64 \sqrt{- a^{9} \cosh (9 c_{1}) x^{15} - a^{9} \sinh (9 c_{1}) x^{15} + 7 a^{8} \cosh (12 c_{1}) x^{12} + 7 a^{8} \sinh (12 c_{1}) x^{12} - 19 a^{7} \cosh (15 c_{1}) x^{9} - 19 a^{7} \sinh (15 c_{1}) x^{9} + 25 a^{6} \cosh (18 c_{1}) x^{6} + 25 a^{6} \sinh (18 c_{1}) x^{6} - 16 a^{5} \cosh (21 c_{1}) x^{3} - 16 a^{5} \sinh (21 c_{1}) x^{3} + 4 a^{4} \cosh (24 c_{1}) + 4 a^{4} \sinh (24 c_{1})}}} - \frac{i \sqrt{3} a^{3} x^{5}}{\sqrt[3]{27 a^{6} x^{12} - 144 a^{5} \cosh (3 c_{1}) x^{9} - 144 a^{5} \sinh (3 c_{1}) x^{9} + 272 a^{4} \cosh (6 c_{1}) x^{6} + 272 a^{4} \sinh (6 c_{1}) x^{6} - 256 a^{3} \cosh (9 c_{1}) x^{3} - 256 a^{3} \sinh (9 c_{1}) x^{3} + 128 a^{2} \cosh (12 c_{1}) + 128 a^{2} \sinh (12 c_{1}) + 64 \sqrt{- a^{9} \cosh (9 c_{1}) x^{15} - a^{9} \sinh (9 c_{1}) x^{15} + 7 a^{8} \cosh (12 c_{1}) x^{12} + 7 a^{8} \sinh (12 c_{1}) x^{12} - 19 a^{7} \cosh (15 c_{1}) x^{9} - 19 a^{7} \sinh (15 c_{1}) x^{9} + 25 a^{6} \cosh (18 c_{1}) x^{6} + 25 a^{6} \sinh (18 c_{1}) x^{6} - 16 a^{5} \cosh (21 c_{1}) x^{3} - 16 a^{5} \sinh (21 c_{1}) x^{3} + 4 a^{4} \cosh (24 c_{1}) + 4 a^{4} \sinh (24 c_{1})}}} + \frac{a^{3} x^{5}}{\sqrt[3]{27 a^{6} x^{12} - 144 a^{5} \cosh (3 c_{1}) x^{9} - 144 a^{5} \sinh (3 c_{1}) x^{9} + 272 a^{4} \cosh (6 c_{1}) x^{6} + 272 a^{4} \sinh (6 c_{1}) x^{6} - 256 a^{3} \cosh (9 c_{1}) x^{3} - 256 a^{3} \sinh (9 c_{1}) x^{3} + 128 a^{2} \cosh (12 c_{1}) + 128 a^{2} \sinh (12 c_{1}) + 64 \sqrt{- a^{9} \cosh (9 c_{1}) x^{15} - a^{9} \sinh (9 c_{1}) x^{15} + 7 a^{8} \cosh (12 c_{1}) x^{12} + 7 a^{8} \sinh (12 c_{1}) x^{12} - 19 a^{7} \cosh (15 c_{1}) x^{9} - 19 a^{7} \sinh (15 c_{1}) x^{9} + 25 a^{6} \cosh (18 c_{1}) x^{6} + 25 a^{6} \sinh (18 c_{1}) x^{6} - 16 a^{5} \cosh (21 c_{1}) x^{3} - 16 a^{5} \sinh (21 c_{1}) x^{3} + 4 a^{4} \cosh (24 c_{1}) + 4 a^{4} \sinh (24 c_{1})}}} + \frac{3}{16} a^{2} \cosh (3 c_{1}) x^{4} - \frac{3}{16} a^{2} \sinh (3 c_{1}) x^{4} + \frac{i \sqrt{3} a^{2} (\cosh (3 c_{1}) + \sinh (3 c_{1})) x^{2}}{\sqrt[3]{27 a^{6} x^{12} - 144 a^{5} \cosh (3 c_{1}) x^{9} - 144 a^{5} \sinh (3 c_{1}) x^{9} + 272 a^{4} \cosh (6 c_{1}) x^{6} + 272 a^{4} \sinh (6 c_{1}) x^{6} - 256 a^{3} \cosh (9 c_{1}) x^{3} - 256 a^{3} \sinh (9 c_{1}) x^{3} + 128 a^{2} \cosh (12 c_{1}) + 128 a^{2} \sinh (12 c_{1}) + 64 \sqrt{- a^{9} \cosh (9 c_{1}) x^{15} - a^{9} \sinh (9 c_{1}) x^{15} + 7 a^{8} \cosh (12 c_{1}) x^{12} + 7 a^{8} \sinh (12 c_{1}) x^{12} - 19 a^{7} \cosh (15 c_{1}) x^{9} - 19 a^{7} \sinh (15 c_{1}) x^{9} + 25 a^{6} \cosh (18 c_{1}) x^{6} + 25 a^{6} \sinh (18 c_{1}) x^{6} - 16 a^{5} \cosh (21 c_{1}) x^{3} - 16 a^{5} \sinh (21 c_{1}) x^{3} + 4 a^{4} \cosh (24 c_{1}) + 4 a^{4} \sinh (24 c_{1})}}} - \frac{a^{2} (\cosh (3 c_{1}) + \sinh (3 c_{1})) x^{2}}{\sqrt[3]{27 a^{6} x^{12} - 144 a^{5} \cosh (3 c_{1}) x^{9} - 144 a^{5} \sinh (3 c_{1}) x^{9} + 272 a^{4} \cosh (6 c_{1}) x^{6} + 272 a^{4} \sinh (6 c_{1}) x^{6} - 256 a^{3} \cosh (9 c_{1}) x^{3} - 256 a^{3} \sinh (9 c_{1}) x^{3} + 128 a^{2} \cosh (12 c_{1}) + 128 a^{2} \sinh (12 c_{1}) + 64 \sqrt{- a^{9} \cosh (9 c_{1}) x^{15} - a^{9} \sinh (9 c_{1}) x^{15} + 7 a^{8} \cosh (12 c_{1}) x^{12} + 7 a^{8} \sinh (12 c_{1}) x^{12} - 19 a^{7} \cosh (15 c_{1}) x^{9} - 19 a^{7} \sinh (15 c_{1}) x^{9} + 25 a^{6} \cosh (18 c_{1}) x^{6} + 25 a^{6} \sinh (18 c_{1}) x^{6} - 16 a^{5} \cosh (21 c_{1}) x^{3} - 16 a^{5} \sinh (21 c_{1}) x^{3} + 4 a^{4} \cosh (24 c_{1}) + 4 a^{4} \sinh (24 c_{1})}}} + a x - \frac{1}{32} i \sqrt{3} (\cosh (3 c_{1}) - \sinh (3 c_{1})) \sqrt[3]{27 a^{6} x^{12} - 144 a^{5} \cosh (3 c_{1}) x^{9} - 144 a^{5} \sinh (3 c_{1}) x^{9} + 272 a^{4} \cosh (6 c_{1}) x^{6} + 272 a^{4} \sinh (6 c_{1}) x^{6} - 256 a^{3} \cosh (9 c_{1}) x^{3} - 256 a^{3} \sinh (9 c_{1}) x^{3} + 128 a^{2} \cosh (12 c_{1}) + 128 a^{2} \sinh (12 c_{1}) + 64 \sqrt{- a^{9} \cosh (9 c_{1}) x^{15} - a^{9} \sinh (9 c_{1}) x^{15} + 7 a^{8} \cosh (12 c_{1}) x^{12} + 7 a^{8} \sinh (12 c_{1}) x^{12} - 19 a^{7} \cosh (15 c_{1}) x^{9} - 19 a^{7} \sinh (15 c_{1}) x^{9} + 25 a^{6} \cosh (18 c_{1}) x^{6} + 25 a^{6} \sinh (18 c_{1}) x^{6} - 16 a^{5} \cosh (21 c_{1}) x^{3} - 16 a^{5} \sinh (21 c_{1}) x^{3} + 4 a^{4} \cosh (24 c_{1}) + 4 a^{4} \sinh (24 c_{1})}} - \frac{1}{32} (\cosh (3 c_{1}) - \sinh (3 c_{1})) \sqrt[3]{27 a^{6} x^{12} - 144 a^{5} \cosh (3 c_{1}) x^{9} - 144 a^{5} \sinh (3 c_{1}) x^{9} + 272 a^{4} \cosh (6 c_{1}) x^{6} + 272 a^{4} \sinh (6 c_{1}) x^{6} - 256 a^{3} \cosh (9 c_{1}) x^{3} - 256 a^{3} \sinh (9 c_{1}) x^{3} + 128 a^{2} \cosh (12 c_{1}) + 128 a^{2} \sinh (12 c_{1}) + 64 \sqrt{- a^{9} \cosh (9 c_{1}) x^{15} - a^{9} \sinh (9 c_{1}) x^{15} + 7 a^{8} \cosh (12 c_{1}) x^{12} + 7 a^{8} \sinh (12 c_{1}) x^{12} - 19 a^{7} \cosh (15 c_{1}) x^{9} - 19 a^{7} \sinh (15 c_{1}) x^{9} + 25 a^{6} \cosh (18 c_{1}) x^{6} + 25 a^{6} \sinh (18 c_{1}) x^{6} - 16 a^{5} \cosh (21 c_{1}) x^{3} - 16 a^{5} \sinh (21 c_{1}) x^{3} + 4 a^{4} \cosh (24 c_{1}) + 4 a^{4} \sinh (24 c_{1})}}}}, {y (x) \to \sqrt{\frac{9 i \sqrt{3} a^{4} (\cosh (3 c_{1}) - \sinh (3 c_{1})) x^{8}}{32 \sqrt[3]{27 a^{6} x^{12} - 144 a^{5} \cosh (3 c_{1}) x^{9} - 144 a^{5} \sinh (3 c_{1}) x^{9} + 272 a^{4} \cosh (6 c_{1}) x^{6} + 272 a^{4} \sinh (6 c_{1}) x^{6} - 256 a^{3} \cosh (9 c_{1}) x^{3} - 256 a^{3} \sinh (9 c_{1}) x^{3} + 128 a^{2} \cosh (12 c_{1}) + 128 a^{2} \sinh (12 c_{1}) + 64 \sqrt{- a^{9} \cosh (9 c_{1}) x^{15} - a^{9} \sinh (9 c_{1}) x^{15} + 7 a^{8} \cosh (12 c_{1}) x^{12} + 7 a^{8} \sinh (12 c_{1}) x^{12} - 19 a^{7} \cosh (15 c_{1}) x^{9} - 19 a^{7} \sinh (15 c_{1}) x^{9} + 25 a^{6} \cosh (18 c_{1}) x^{6} + 25 a^{6} \sinh (18 c_{1}) x^{6} - 16 a^{5} \cosh (21 c_{1}) x^{3} - 16 a^{5} \sinh (21 c_{1}) x^{3} + 4 a^{4} \cosh (24 c_{1}) + 4 a^{4} \sinh (24 c_{1})}}} - \frac{9 a^{4} (\cosh (3 c_{1}) - \sinh (3 c_{1})) x^{8}}{32 \sqrt[3]{27 a^{6} x^{12} - 144 a^{5} \cosh (3 c_{1}) x^{9} - 144 a^{5} \sinh (3 c_{1}) x^{9} + 272 a^{4} \cosh (6 c_{1}) x^{6} + 272 a^{4} \sinh (6 c_{1}) x^{6} - 256 a^{3} \cosh (9 c_{1}) x^{3} - 256 a^{3} \sinh (9 c_{1}) x^{3} + 128 a^{2} \cosh (12 c_{1}) + 128 a^{2} \sinh (12 c_{1}) + 64 \sqrt{- a^{9} \cosh (9 c_{1}) x^{15} - a^{9} \sinh (9 c_{1}) x^{15} + 7 a^{8} \cosh (12 c_{1}) x^{12} + 7 a^{8} \sinh (12 c_{1}) x^{12} - 19 a^{7} \cosh (15 c_{1}) x^{9} - 19 a^{7} \sinh (15 c_{1}) x^{9} + 25 a^{6} \cosh (18 c_{1}) x^{6} + 25 a^{6} \sinh (18 c_{1}) x^{6} - 16 a^{5} \cosh (21 c_{1}) x^{3} - 16 a^{5} \sinh (21 c_{1}) x^{3} + 4 a^{4} \cosh (24 c_{1}) + 4 a^{4} \sinh (24 c_{1})}}} - \frac{i \sqrt{3} a^{3} x^{5}}{\sqrt[3]{27 a^{6} x^{12} - 144 a^{5} \cosh (3 c_{1}) x^{9} - 144 a^{5} \sinh (3 c_{1}) x^{9} + 272 a^{4} \cosh (6 c_{1}) x^{6} + 272 a^{4} \sinh (6 c_{1}) x^{6} - 256 a^{3} \cosh (9 c_{1}) x^{3} - 256 a^{3} \sinh (9 c_{1}) x^{3} + 128 a^{2} \cosh (12 c_{1}) + 128 a^{2} \sinh (12 c_{1}) + 64 \sqrt{- a^{9} \cosh (9 c_{1}) x^{15} - a^{9} \sinh (9 c_{1}) x^{15} + 7 a^{8} \cosh (12 c_{1}) x^{12} + 7 a^{8} \sinh (12 c_{1}) x^{12} - 19 a^{7} \cosh (15 c_{1}) x^{9} - 19 a^{7} \sinh (15 c_{1}) x^{9} + 25 a^{6} \cosh (18 c_{1}) x^{6} + 25 a^{6} \sinh (18 c_{1}) x^{6} - 16 a^{5} \cosh (21 c_{1}) x^{3} - 16 a^{5} \sinh (21 c_{1}) x^{3} + 4 a^{4} \cosh (24 c_{1}) + 4 a^{4} \sinh (24 c_{1})}}} + \frac{a^{3} x^{5}}{\sqrt[3]{27 a^{6} x^{12} - 144 a^{5} \cosh (3 c_{1}) x^{9} - 144 a^{5} \sinh (3 c_{1}) x^{9} + 272 a^{4} \cosh (6 c_{1}) x^{6} + 272 a^{4} \sinh (6 c_{1}) x^{6} - 256 a^{3} \cosh (9 c_{1}) x^{3} - 256 a^{3} \sinh (9 c_{1}) x^{3} + 128 a^{2} \cosh (12 c_{1}) + 128 a^{2} \sinh (12 c_{1}) + 64 \sqrt{- a^{9} \cosh (9 c_{1}) x^{15} - a^{9} \sinh (9 c_{1}) x^{15} + 7 a^{8} \cosh (12 c_{1}) x^{12} + 7 a^{8} \sinh (12 c_{1}) x^{12} - 19 a^{7} \cosh (15 c_{1}) x^{9} - 19 a^{7} \sinh (15 c_{1}) x^{9} + 25 a^{6} \cosh (18 c_{1}) x^{6} + 25 a^{6} \sinh (18 c_{1}) x^{6} - 16 a^{5} \cosh (21 c_{1}) x^{3} - 16 a^{5} \sinh (21 c_{1}) x^{3} + 4 a^{4} \cosh (24 c_{1}) + 4 a^{4} \sinh (24 c_{1})}}} + \frac{3}{16} a^{2} \cosh (3 c_{1}) x^{4} - \frac{3}{16} a^{2} \sinh (3 c_{1}) x^{4} + \frac{i \sqrt{3} a^{2} (\cosh (3 c_{1}) + \sinh (3 c_{1})) x^{2}}{\sqrt[3]{27 a^{6} x^{12} - 144 a^{5} \cosh (3 c_{1}) x^{9} - 144 a^{5} \sinh (3 c_{1}) x^{9} + 272 a^{4} \cosh (6 c_{1}) x^{6} + 272 a^{4} \sinh (6 c_{1}) x^{6} - 256 a^{3} \cosh (9 c_{1}) x^{3} - 256 a^{3} \sinh (9 c_{1}) x^{3} + 128 a^{2} \cosh (12 c_{1}) + 128 a^{2} \sinh (12 c_{1}) + 64 \sqrt{- a^{9} \cosh (9 c_{1}) x^{15} - a^{9} \sinh (9 c_{1}) x^{15} + 7 a^{8} \cosh (12 c_{1}) x^{12} + 7 a^{8} \sinh (12 c_{1}) x^{12} - 19 a^{7} \cosh (15 c_{1}) x^{9} - 19 a^{7} \sinh (15 c_{1}) x^{9} + 25 a^{6} \cosh (18 c_{1}) x^{6} + 25 a^{6} \sinh (18 c_{1}) x^{6} - 16 a^{5} \cosh (21 c_{1}) x^{3} - 16 a^{5} \sinh (21 c_{1}) x^{3} + 4 a^{4} \cosh (24 c_{1}) + 4 a^{4} \sinh (24 c_{1})}}} - \frac{a^{2} (\cosh (3 c_{1}) + \sinh (3 c_{1})) x^{2}}{\sqrt[3]{27 a^{6} x^{12} - 144 a^{5} \cosh (3 c_{1}) x^{9} - 144 a^{5} \sinh (3 c_{1}) x^{9} + 272 a^{4} \cosh (6 c_{1}) x^{6} + 272 a^{4} \sinh (6 c_{1}) x^{6} - 256 a^{3} \cosh (9 c_{1}) x^{3} - 256 a^{3} \sinh (9 c_{1}) x^{3} + 128 a^{2} \cosh (12 c_{1}) + 128 a^{2} \sinh (12 c_{1}) + 64 \sqrt{- a^{9} \cosh (9 c_{1}) x^{15} - a^{9} \sinh (9 c_{1}) x^{15} + 7 a^{8} \cosh (12 c_{1}) x^{12} + 7 a^{8} \sinh (12 c_{1}) x^{12} - 19 a^{7} \cosh (15 c_{1}) x^{9} - 19 a^{7} \sinh (15 c_{1}) x^{9} + 25 a^{6} \cosh (18 c_{1}) x^{6} + 25 a^{6} \sinh (18 c_{1}) x^{6} - 16 a^{5} \cosh (21 c_{1}) x^{3} - 16 a^{5} \sinh (21 c_{1}) x^{3} + 4 a^{4} \cosh (24 c_{1}) + 4 a^{4} \sinh (24 c_{1})}}} + a x - \frac{1}{32} i \sqrt{3} (\cosh (3 c_{1}) - \sinh (3 c_{1})) \sqrt[3]{27 a^{6} x^{12} - 144 a^{5} \cosh (3 c_{1}) x^{9} - 144 a^{5} \sinh (3 c_{1}) x^{9} + 272 a^{4} \cosh (6 c_{1}) x^{6} + 272 a^{4} \sinh (6 c_{1}) x^{6} - 256 a^{3} \cosh (9 c_{1}) x^{3} - 256 a^{3} \sinh (9 c_{1}) x^{3} + 128 a^{2} \cosh (12 c_{1}) + 128 a^{2} \sinh (12 c_{1}) + 64 \sqrt{- a^{9} \cosh (9 c_{1}) x^{15} - a^{9} \sinh (9 c_{1}) x^{15} + 7 a^{8} \cosh (12 c_{1}) x^{12} + 7 a^{8} \sinh (12 c_{1}) x^{12} - 19 a^{7} \cosh (15 c_{1}) x^{9} - 19 a^{7} \sinh (15 c_{1}) x^{9} + 25 a^{6} \cosh (18 c_{1}) x^{6} + 25 a^{6} \sinh (18 c_{1}) x^{6} - 16 a^{5} \cosh (21 c_{1}) x^{3} - 16 a^{5} \sinh (21 c_{1}) x^{3} + 4 a^{4} \cosh (24 c_{1}) + 4 a^{4} \sinh (24 c_{1})}} - \frac{1}{32} (\cosh (3 c_{1}) - \sinh (3 c_{1})) \sqrt[3]{27 a^{6} x^{12} - 144 a^{5} \cosh (3 c_{1}) x^{9} - 144 a^{5} \sinh (3 c_{1}) x^{9} + 272 a^{4} \cosh (6 c_{1}) x^{6} + 272 a^{4} \sinh (6 c_{1}) x^{6} - 256 a^{3} \cosh (9 c_{1}) x^{3} - 256 a^{3} \sinh (9 c_{1}) x^{3} + 128 a^{2} \cosh (12 c_{1}) + 128 a^{2} \sinh (12 c_{1}) + 64 \sqrt{- a^{9} \cosh (9 c_{1}) x^{15} - a^{9} \sinh (9 c_{1}) x^{15} + 7 a^{8} \cosh (12 c_{1}) x^{12} + 7 a^{8} \sinh (12 c_{1}) x^{12} - 19 a^{7} \cosh (15 c_{1}) x^{9} - 19 a^{7} \sinh (15 c_{1}) x^{9} + 25 a^{6} \cosh (18 c_{1}) x^{6} + 25 a^{6} \sinh (18 c_{1}) x^{6} - 16 a^{5} \cosh (21 c_{1}) x^{3} - 16 a^{5} \sinh (21 c_{1}) x^{3} + 4 a^{4} \cosh (24 c_{1}) + 4 a^{4} \sinh (24 c_{1})}}}}, {y (x) \to - \sqrt{- \frac{9 i \sqrt{3} a^{4} (\cosh (3 c_{1}) - \sinh (3 c_{1})) x^{8}}{32 \sqrt[3]{27 a^{6} x^{12} - 144 a^{5} \cosh (3 c_{1}) x^{9} - 144 a^{5} \sinh (3 c_{1}) x^{9} + 272 a^{4} \cosh (6 c_{1}) x^{6} + 272 a^{4} \sinh (6 c_{1}) x^{6} - 256 a^{3} \cosh (9 c_{1}) x^{3} - 256 a^{3} \sinh (9 c_{1}) x^{3} + 128 a^{2} \cosh (12 c_{1}) + 128 a^{2} \sinh (12 c_{1}) + 64 \sqrt{- a^{9} \cosh (9 c_{1}) x^{15} - a^{9} \sinh (9 c_{1}) x^{15} + 7 a^{8} \cosh (12 c_{1}) x^{12} + 7 a^{8} \sinh (12 c_{1}) x^{12} - 19 a^{7} \cosh (15 c_{1}) x^{9} - 19 a^{7} \sinh (15 c_{1}) x^{9} + 25 a^{6} \cosh (18 c_{1}) x^{6} + 25 a^{6} \sinh (18 c_{1}) x^{6} - 16 a^{5} \cosh (21 c_{1}) x^{3} - 16 a^{5} \sinh (21 c_{1}) x^{3} + 4 a^{4} \cosh (24 c_{1}) + 4 a^{4} \sinh (24 c_{1})}}} - \frac{9 a^{4} (\cosh (3 c_{1}) - \sinh (3 c_{1})) x^{8}}{32 \sqrt[3]{27 a^{6} x^{12} - 144 a^{5} \cosh (3 c_{1}) x^{9} - 144 a^{5} \sinh (3 c_{1}) x^{9} + 272 a^{4} \cosh (6 c_{1}) x^{6} + 272 a^{4} \sinh (6 c_{1}) x^{6} - 256 a^{3} \cosh (9 c_{1}) x^{3} - 256 a^{3} \sinh (9 c_{1}) x^{3} + 128 a^{2} \cosh (12 c_{1}) + 128 a^{2} \sinh (12 c_{1}) + 64 \sqrt{- a^{9} \cosh (9 c_{1}) x^{15} - a^{9} \sinh (9 c_{1}) x^{15} + 7 a^{8} \cosh (12 c_{1}) x^{12} + 7 a^{8} \sinh (12 c_{1}) x^{12} - 19 a^{7} \cosh (15 c_{1}) x^{9} - 19 a^{7} \sinh (15 c_{1}) x^{9} + 25 a^{6} \cosh (18 c_{1}) x^{6} + 25 a^{6} \sinh (18 c_{1}) x^{6} - 16 a^{5} \cosh (21 c_{1}) x^{3} - 16 a^{5} \sinh (21 c_{1}) x^{3} + 4 a^{4} \cosh (24 c_{1}) + 4 a^{4} \sinh (24 c_{1})}}} + \frac{i \sqrt{3} a^{3} x^{5}}{\sqrt[3]{27 a^{6} x^{12} - 144 a^{5} \cosh (3 c_{1}) x^{9} - 144 a^{5} \sinh (3 c_{1}) x^{9} + 272 a^{4} \cosh (6 c_{1}) x^{6} + 272 a^{4} \sinh (6 c_{1}) x^{6} - 256 a^{3} \cosh (9 c_{1}) x^{3} - 256 a^{3} \sinh (9 c_{1}) x^{3} + 128 a^{2} \cosh (12 c_{1}) + 128 a^{2} \sinh (12 c_{1}) + 64 \sqrt{- a^{9} \cosh (9 c_{1}) x^{15} - a^{9} \sinh (9 c_{1}) x^{15} + 7 a^{8} \cosh (12 c_{1}) x^{12} + 7 a^{8} \sinh (12 c_{1}) x^{12} - 19 a^{7} \cosh (15 c_{1}) x^{9} - 19 a^{7} \sinh (15 c_{1}) x^{9} + 25 a^{6} \cosh (18 c_{1}) x^{6} + 25 a^{6} \sinh (18 c_{1}) x^{6} - 16 a^{5} \cosh (21 c_{1}) x^{3} - 16 a^{5} \sinh (21 c_{1}) x^{3} + 4 a^{4} \cosh (24 c_{1}) + 4 a^{4} \sinh (24 c_{1})}}} + \frac{a^{3} x^{5}}{\sqrt[3]{27 a^{6} x^{12} - 144 a^{5} \cosh (3 c_{1}) x^{9} - 144 a^{5} \sinh (3 c_{1}) x^{9} + 272 a^{4} \cosh (6 c_{1}) x^{6} + 272 a^{4} \sinh (6 c_{1}) x^{6} - 256 a^{3} \cosh (9 c_{1}) x^{3} - 256 a^{3} \sinh (9 c_{1}) x^{3} + 128 a^{2} \cosh (12 c_{1}) + 128 a^{2} \sinh (12 c_{1}) + 64 \sqrt{- a^{9} \cosh (9 c_{1}) x^{15} - a^{9} \sinh (9 c_{1}) x^{15} + 7 a^{8} \cosh (12 c_{1}) x^{12} + 7 a^{8} \sinh (12 c_{1}) x^{12} - 19 a^{7} \cosh (15 c_{1}) x^{9} - 19 a^{7} \sinh (15 c_{1}) x^{9} + 25 a^{6} \cosh (18 c_{1}) x^{6} + 25 a^{6} \sinh (18 c_{1}) x^{6} - 16 a^{5} \cosh (21 c_{1}) x^{3} - 16 a^{5} \sinh (21 c_{1}) x^{3} + 4 a^{4} \cosh (24 c_{1}) + 4 a^{4} \sinh (24 c_{1})}}} + \frac{3}{16} a^{2} \cosh (3 c_{1}) x^{4} - \frac{3}{16} a^{2} \sinh (3 c_{1}) x^{4} - \frac{i \sqrt{3} a^{2} (\cosh (3 c_{1}) + \sinh (3 c_{1})) x^{2}}{\sqrt[3]{27 a^{6} x^{12} - 144 a^{5} \cosh (3 c_{1}) x^{9} - 144 a^{5} \sinh (3 c_{1}) x^{9} + 272 a^{4} \cosh (6 c_{1}) x^{6} + 272 a^{4} \sinh (6 c_{1}) x^{6} - 256 a^{3} \cosh (9 c_{1}) x^{3} - 256 a^{3} \sinh (9 c_{1}) x^{3} + 128 a^{2} \cosh (12 c_{1}) + 128 a^{2} \sinh (12 c_{1}) + 64 \sqrt{- a^{9} \cosh (9 c_{1}) x^{15} - a^{9} \sinh (9 c_{1}) x^{15} + 7 a^{8} \cosh (12 c_{1}) x^{12} + 7 a^{8} \sinh (12 c_{1}) x^{12} - 19 a^{7} \cosh (15 c_{1}) x^{9} - 19 a^{7} \sinh (15 c_{1}) x^{9} + 25 a^{6} \cosh (18 c_{1}) x^{6} + 25 a^{6} \sinh (18 c_{1}) x^{6} - 16 a^{5} \cosh (21 c_{1}) x^{3} - 16 a^{5} \sinh (21 c_{1}) x^{3} + 4 a^{4} \cosh (24 c_{1}) + 4 a^{4} \sinh (24 c_{1})}}} - \frac{a^{2} (\cosh (3 c_{1}) + \sinh (3 c_{1})) x^{2}}{\sqrt[3]{27 a^{6} x^{12} - 144 a^{5} \cosh (3 c_{1}) x^{9} - 144 a^{5} \sinh (3 c_{1}) x^{9} + 272 a^{4} \cosh (6 c_{1}) x^{6} + 272 a^{4} \sinh (6 c_{1}) x^{6} - 256 a^{3} \cosh (9 c_{1}) x^{3} - 256 a^{3} \sinh (9 c_{1}) x^{3} + 128 a^{2} \cosh (12 c_{1}) + 128 a^{2} \sinh (12 c_{1}) + 64 \sqrt{- a^{9} \cosh (9 c_{1}) x^{15} - a^{9} \sinh (9 c_{1}) x^{15} + 7 a^{8} \cosh (12 c_{1}) x^{12} + 7 a^{8} \sinh (12 c_{1}) x^{12} - 19 a^{7} \cosh (15 c_{1}) x^{9} - 19 a^{7} \sinh (15 c_{1}) x^{9} + 25 a^{6} \cosh (18 c_{1}) x^{6} + 25 a^{6} \sinh (18 c_{1}) x^{6} - 16 a^{5} \cosh (21 c_{1}) x^{3} - 16 a^{5} \sinh (21 c_{1}) x^{3} + 4 a^{4} \cosh (24 c_{1}) + 4 a^{4} \sinh (24 c_{1})}}} + a x + \frac{1}{32} i \sqrt{3} (\cosh (3 c_{1}) - \sinh (3 c_{1})) \sqrt[3]{27 a^{6} x^{12} - 144 a^{5} \cosh (3 c_{1}) x^{9} - 144 a^{5} \sinh (3 c_{1}) x^{9} + 272 a^{4} \cosh (6 c_{1}) x^{6} + 272 a^{4} \sinh (6 c_{1}) x^{6} - 256 a^{3} \cosh (9 c_{1}) x^{3} - 256 a^{3} \sinh (9 c_{1}) x^{3} + 128 a^{2} \cosh (12 c_{1}) + 128 a^{2} \sinh (12 c_{1}) + 64 \sqrt{- a^{9} \cosh (9 c_{1}) x^{15} - a^{9} \sinh (9 c_{1}) x^{15} + 7 a^{8} \cosh (12 c_{1}) x^{12} + 7 a^{8} \sinh (12 c_{1}) x^{12} - 19 a^{7} \cosh (15 c_{1}) x^{9} - 19 a^{7} \sinh (15 c_{1}) x^{9} + 25 a^{6} \cosh (18 c_{1}) x^{6} + 25 a^{6} \sinh (18 c_{1}) x^{6} - 16 a^{5} \cosh (21 c_{1}) x^{3} - 16 a^{5} \sinh (21 c_{1}) x^{3} + 4 a^{4} \cosh (24 c_{1}) + 4 a^{4} \sinh (24 c_{1})}} - \frac{1}{32} (\cosh (3 c_{1}) - \sinh (3 c_{1})) \sqrt[3]{27 a^{6} x^{12} - 144 a^{5} \cosh (3 c_{1}) x^{9} - 144 a^{5} \sinh (3 c_{1}) x^{9} + 272 a^{4} \cosh (6 c_{1}) x^{6} + 272 a^{4} \sinh (6 c_{1}) x^{6} - 256 a^{3} \cosh (9 c_{1}) x^{3} - 256 a^{3} \sinh (9 c_{1}) x^{3} + 128 a^{2} \cosh (12 c_{1}) + 128 a^{2} \sinh (12 c_{1}) + 64 \sqrt{- a^{9} \cosh (9 c_{1}) x^{15} - a^{9} \sinh (9 c_{1}) x^{15} + 7 a^{8} \cosh (12 c_{1}) x^{12} + 7 a^{8} \sinh (12 c_{1}) x^{12} - 19 a^{7} \cosh (15 c_{1}) x^{9} - 19 a^{7} \sinh (15 c_{1}) x^{9} + 25 a^{6} \cosh (18 c_{1}) x^{6} + 25 a^{6} \sinh (18 c_{1}) x^{6} - 16 a^{5} \cosh (21 c_{1}) x^{3} - 16 a^{5} \sinh (21 c_{1}) x^{3} + 4 a^{4} \cosh (24 c_{1}) + 4 a^{4} \sinh (24 c_{1})}}}}, {y (x) \to \sqrt{- \frac{9 i \sqrt{3} a^{4} (\cosh (3 c_{1}) - \sinh (3 c_{1})) x^{8}}{32 \sqrt[3]{27 a^{6} x^{12} - 144 a^{5} \cosh (3 c_{1}) x^{9} - 144 a^{5} \sinh (3 c_{1}) x^{9} + 272 a^{4} \cosh (6 c_{1}) x^{6} + 272 a^{4} \sinh (6 c_{1}) x^{6} - 256 a^{3} \cosh (9 c_{1}) x^{3} - 256 a^{3} \sinh (9 c_{1}) x^{3} + 128 a^{2} \cosh (12 c_{1}) + 128 a^{2} \sinh (12 c_{1}) + 64 \sqrt{- a^{9} \cosh (9 c_{1}) x^{15} - a^{9} \sinh (9 c_{1}) x^{15} + 7 a^{8} \cosh (12 c_{1}) x^{12} + 7 a^{8} \sinh (12 c_{1}) x^{12} - 19 a^{7} \cosh (15 c_{1}) x^{9} - 19 a^{7} \sinh (15 c_{1}) x^{9} + 25 a^{6} \cosh (18 c_{1}) x^{6} + 25 a^{6} \sinh (18 c_{1}) x^{6} - 16 a^{5} \cosh (21 c_{1}) x^{3} - 16 a^{5} \sinh (21 c_{1}) x^{3} + 4 a^{4} \cosh (24 c_{1}) + 4 a^{4} \sinh (24 c_{1})}}} - \frac{9 a^{4} (\cosh (3 c_{1}) - \sinh (3 c_{1})) x^{8}}{32 \sqrt[3]{27 a^{6} x^{12} - 144 a^{5} \cosh (3 c_{1}) x^{9} - 144 a^{5} \sinh (3 c_{1}) x^{9} + 272 a^{4} \cosh (6 c_{1}) x^{6} + 272 a^{4} \sinh (6 c_{1}) x^{6} - 256 a^{3} \cosh (9 c_{1}) x^{3} - 256 a^{3} \sinh (9 c_{1}) x^{3} + 128 a^{2} \cosh (12 c_{1}) + 128 a^{2} \sinh (12 c_{1}) + 64 \sqrt{- a^{9} \cosh (9 c_{1}) x^{15} - a^{9} \sinh (9 c_{1}) x^{15} + 7 a^{8} \cosh (12 c_{1}) x^{12} + 7 a^{8} \sinh (12 c_{1}) x^{12} - 19 a^{7} \cosh (15 c_{1}) x^{9} - 19 a^{7} \sinh (15 c_{1}) x^{9} + 25 a^{6} \cosh (18 c_{1}) x^{6} + 25 a^{6} \sinh (18 c_{1}) x^{6} - 16 a^{5} \cosh (21 c_{1}) x^{3} - 16 a^{5} \sinh (21 c_{1}) x^{3} + 4 a^{4} \cosh (24 c_{1}) + 4 a^{4} \sinh (24 c_{1})}}} + \frac{i \sqrt{3} a^{3} x^{5}}{\sqrt[3]{27 a^{6} x^{12} - 144 a^{5} \cosh (3 c_{1}) x^{9} - 144 a^{5} \sinh (3 c_{1}) x^{9} + 272 a^{4} \cosh (6 c_{1}) x^{6} + 272 a^{4} \sinh (6 c_{1}) x^{6} - 256 a^{3} \cosh (9 c_{1}) x^{3} - 256 a^{3} \sinh (9 c_{1}) x^{3} + 128 a^{2} \cosh (12 c_{1}) + 128 a^{2} \sinh (12 c_{1}) + 64 \sqrt{- a^{9} \cosh (9 c_{1}) x^{15} - a^{9} \sinh (9 c_{1}) x^{15} + 7 a^{8} \cosh (12 c_{1}) x^{12} + 7 a^{8} \sinh (12 c_{1}) x^{12} - 19 a^{7} \cosh (15 c_{1}) x^{9} - 19 a^{7} \sinh (15 c_{1}) x^{9} + 25 a^{6} \cosh (18 c_{1}) x^{6} + 25 a^{6} \sinh (18 c_{1}) x^{6} - 16 a^{5} \cosh (21 c_{1}) x^{3} - 16 a^{5} \sinh (21 c_{1}) x^{3} + 4 a^{4} \cosh (24 c_{1}) + 4 a^{4} \sinh (24 c_{1})}}} + \frac{a^{3} x^{5}}{\sqrt[3]{27 a^{6} x^{12} - 144 a^{5} \cosh (3 c_{1}) x^{9} - 144 a^{5} \sinh (3 c_{1}) x^{9} + 272 a^{4} \cosh (6 c_{1}) x^{6} + 272 a^{4} \sinh (6 c_{1}) x^{6} - 256 a^{3} \cosh (9 c_{1}) x^{3} - 256 a^{3} \sinh (9 c_{1}) x^{3} + 128 a^{2} \cosh (12 c_{1}) + 128 a^{2} \sinh (12 c_{1}) + 64 \sqrt{- a^{9} \cosh (9 c_{1}) x^{15} - a^{9} \sinh (9 c_{1}) x^{15} + 7 a^{8} \cosh (12 c_{1}) x^{12} + 7 a^{8} \sinh (12 c_{1}) x^{12} - 19 a^{7} \cosh (15 c_{1}) x^{9} - 19 a^{7} \sinh (15 c_{1}) x^{9} + 25 a^{6} \cosh (18 c_{1}) x^{6} + 25 a^{6} \sinh (18 c_{1}) x^{6} - 16 a^{5} \cosh (21 c_{1}) x^{3} - 16 a^{5} \sinh (21 c_{1}) x^{3} + 4 a^{4} \cosh (24 c_{1}) + 4 a^{4} \sinh (24 c_{1})}}} + \frac{3}{16} a^{2} \cosh (3 c_{1}) x^{4} - \frac{3}{16} a^{2} \sinh (3 c_{1}) x^{4} - \frac{i \sqrt{3} a^{2} (\cosh (3 c_{1}) + \sinh (3 c_{1})) x^{2}}{\sqrt[3]{27 a^{6} x^{12} - 144 a^{5} \cosh (3 c_{1}) x^{9} - 144 a^{5} \sinh (3 c_{1}) x^{9} + 272 a^{4} \cosh (6 c_{1}) x^{6} + 272 a^{4} \sinh (6 c_{1}) x^{6} - 256 a^{3} \cosh (9 c_{1}) x^{3} - 256 a^{3} \sinh (9 c_{1}) x^{3} + 128 a^{2} \cosh (12 c_{1}) + 128 a^{2} \sinh (12 c_{1}) + 64 \sqrt{- a^{9} \cosh (9 c_{1}) x^{15} - a^{9} \sinh (9 c_{1}) x^{15} + 7 a^{8} \cosh (12 c_{1}) x^{12} + 7 a^{8} \sinh (12 c_{1}) x^{12} - 19 a^{7} \cosh (15 c_{1}) x^{9} - 19 a^{7} \sinh (15 c_{1}) x^{9} + 25 a^{6} \cosh (18 c_{1}) x^{6} + 25 a^{6} \sinh (18 c_{1}) x^{6} - 16 a^{5} \cosh (21 c_{1}) x^{3} - 16 a^{5} \sinh (21 c_{1}) x^{3} + 4 a^{4} \cosh (24 c_{1}) + 4 a^{4} \sinh (24 c_{1})}}} - \frac{a^{2} (\cosh (3 c_{1}) + \sinh (3 c_{1})) x^{2}}{\sqrt[3]{27 a^{6} x^{12} - 144 a^{5} \cosh (3 c_{1}) x^{9} - 144 a^{5} \sinh (3 c_{1}) x^{9} + 272 a^{4} \cosh (6 c_{1}) x^{6} + 272 a^{4} \sinh (6 c_{1}) x^{6} - 256 a^{3} \cosh (9 c_{1}) x^{3} - 256 a^{3} \sinh (9 c_{1}) x^{3} + 128 a^{2} \cosh (12 c_{1}) + 128 a^{2} \sinh (12 c_{1}) + 64 \sqrt{- a^{9} \cosh (9 c_{1}) x^{15} - a^{9} \sinh (9 c_{1}) x^{15} + 7 a^{8} \cosh (12 c_{1}) x^{12} + 7 a^{8} \sinh (12 c_{1}) x^{12} - 19 a^{7} \cosh (15 c_{1}) x^{9} - 19 a^{7} \sinh (15 c_{1}) x^{9} + 25 a^{6} \cosh (18 c_{1}) x^{6} + 25 a^{6} \sinh (18 c_{1}) x^{6} - 16 a^{5} \cosh (21 c_{1}) x^{3} - 16 a^{5} \sinh (21 c_{1}) x^{3} + 4 a^{4} \cosh (24 c_{1}) + 4 a^{4} \sinh (24 c_{1})}}} + a x + \frac{1}{32} i \sqrt{3} (\cosh (3 c_{1}) - \sinh (3 c_{1})) \sqrt[3]{27 a^{6} x^{12} - 144 a^{5} \cosh (3 c_{1}) x^{9} - 144 a^{5} \sinh (3 c_{1}) x^{9} + 272 a^{4} \cosh (6 c_{1}) x^{6} + 272 a^{4} \sinh (6 c_{1}) x^{6} - 256 a^{3} \cosh (9 c_{1}) x^{3} - 256 a^{3} \sinh (9 c_{1}) x^{3} + 128 a^{2} \cosh (12 c_{1}) + 128 a^{2} \sinh (12 c_{1}) + 64 \sqrt{- a^{9} \cosh (9 c_{1}) x^{15} - a^{9} \sinh (9 c_{1}) x^{15} + 7 a^{8} \cosh (12 c_{1}) x^{12} + 7 a^{8} \sinh (12 c_{1}) x^{12} - 19 a^{7} \cosh (15 c_{1}) x^{9} - 19 a^{7} \sinh (15 c_{1}) x^{9} + 25 a^{6} \cosh (18 c_{1}) x^{6} + 25 a^{6} \sinh (18 c_{1}) x^{6} - 16 a^{5} \cosh (21 c_{1}) x^{3} - 16 a^{5} \sinh (21 c_{1}) x^{3} + 4 a^{4} \cosh (24 c_{1}) + 4 a^{4} \sinh (24 c_{1})}} - \frac{1}{32} (\cosh (3 c_{1}) - \sinh (3 c_{1})) \sqrt[3]{27 a^{6} x^{12} - 144 a^{5} \cosh (3 c_{1}) x^{9} - 144 a^{5} \sinh (3 c_{1}) x^{9} + 272 a^{4} \cosh (6 c_{1}) x^{6} + 272 a^{4} \sinh (6 c_{1}) x^{6} - 256 a^{3} \cosh (9 c_{1}) x^{3} - 256 a^{3} \sinh (9 c_{1}) x^{3} + 128 a^{2} \cosh (12 c_{1}) + 128 a^{2} \sinh (12 c_{1}) + 64 \sqrt{- a^{9} \cosh (9 c_{1}) x^{15} - a^{9} \sinh (9 c_{1}) x^{15} + 7 a^{8} \cosh (12 c_{1}) x^{12} + 7 a^{8} \sinh (12 c_{1}) x^{12} - 19 a^{7} \cosh (15 c_{1}) x^{9} - 19 a^{7} \sinh (15 c_{1}) x^{9} + 25 a^{6} \cosh (18 c_{1}) x^{6} + 25 a^{6} \sinh (18 c_{1}) x^{6} - 16 a^{5} \cosh (21 c_{1}) x^{3} - 16 a^{5} \sinh (21 c_{1}) x^{3} + 4 a^{4} \cosh (24 c_{1}) + 4 a^{4} \sinh (24 c_{1})}}}}}$

Maple: cpu = 0.546 (sec), leaf count = 897 ${y (x) = \frac{x}{2} (\frac{1}{6_C 1} \sqrt[3]{- 36 a {_C 1}^{2} + 8 x^{3} + 12 \sqrt{a (9 a {_C 1}^{2} - 4 x^{3})}_C 1} + \frac{2 x^{2}}{3_C 1} \frac{1}{\sqrt[3]{- 36 a {_C 1}^{2} + 8 x^{3} + 12 \sqrt{a (9 a {_C 1}^{2} - 4 x^{3})}_C 1}} + \frac{x}{3_C 1}) + \frac{a}{2} {(\frac{1}{6_C 1} \sqrt[3]{- 36 a {_C 1}^{2} + 8 x^{3} + 12 \sqrt{a (9 a {_C 1}^{2} - 4 x^{3})}_C 1} + \frac{2 x^{2}}{3_C 1} \frac{1}{\sqrt[3]{- 36 a {_C 1}^{2} + 8 x^{3} + 12 \sqrt{a (9 a {_C 1}^{2} - 4 x^{3})}_C 1}} + \frac{x}{3_C 1})}^{- 1}, y (x) = \frac{x}{2} (- \frac{1}{12_C 1} \sqrt[3]{- 36 a {_C 1}^{2} + 8 x^{3} + 12 \sqrt{a (9 a {_C 1}^{2} - 4 x^{3})}_C 1} - \frac{x^{2}}{3_C 1} \frac{1}{\sqrt[3]{- 36 a {_C 1}^{2} + 8 x^{3} + 12 \sqrt{a (9 a {_C 1}^{2} - 4 x^{3})}_C 1}} + \frac{x}{3_C 1} - \frac{i}{2} \sqrt{3} (\frac{1}{6_C 1} \sqrt[3]{- 36 a {_C 1}^{2} + 8 x^{3} + 12 \sqrt{a (9 a {_C 1}^{2} - 4 x^{3})}_C 1} - \frac{2 x^{2}}{3_C 1} \frac{1}{\sqrt[3]{- 36 a {_C 1}^{2} + 8 x^{3} + 12 \sqrt{a (9 a {_C 1}^{2} - 4 x^{3})}_C 1}})) + \frac{a}{2} {(- \frac{1}{12_C 1} \sqrt[3]{- 36 a {_C 1}^{2} + 8 x^{3} + 12 \sqrt{a (9 a {_C 1}^{2} - 4 x^{3})}_C 1} - \frac{x^{2}}{3_C 1} \frac{1}{\sqrt[3]{- 36 a {_C 1}^{2} + 8 x^{3} + 12 \sqrt{a (9 a {_C 1}^{2} - 4 x^{3})}_C 1}} + \frac{x}{3_C 1} - \frac{i}{2} \sqrt{3} (\frac{1}{6_C 1} \sqrt[3]{- 36 a {_C 1}^{2} + 8 x^{3} + 12 \sqrt{a (9 a {_C 1}^{2} - 4 x^{3})}_C 1} - \frac{2 x^{2}}{3_C 1} \frac{1}{\sqrt[3]{- 36 a {_C 1}^{2} + 8 x^{3} + 12 \sqrt{a (9 a {_C 1}^{2} - 4 x^{3})}_C 1}}))}^{- 1}, y (x) = \frac{x}{2} (- \frac{1}{12_C 1} \sqrt[3]{- 36 a {_C 1}^{2} + 8 x^{3} + 12 \sqrt{a (9 a {_C 1}^{2} - 4 x^{3})}_C 1} - \frac{x^{2}}{3_C 1} \frac{1}{\sqrt[3]{- 36 a {_C 1}^{2} + 8 x^{3} + 12 \sqrt{a (9 a {_C 1}^{2} - 4 x^{3})}_C 1}} + \frac{x}{3_C 1} + \frac{i}{2} \sqrt{3} (\frac{1}{6_C 1} \sqrt[3]{- 36 a {_C 1}^{2} + 8 x^{3} + 12 \sqrt{a (9 a {_C 1}^{2} - 4 x^{3})}_C 1} - \frac{2 x^{2}}{3_C 1} \frac{1}{\sqrt[3]{- 36 a {_C 1}^{2} + 8 x^{3} + 12 \sqrt{a (9 a {_C 1}^{2} - 4 x^{3})}_C 1}})) + \frac{a}{2} {(- \frac{1}{12_C 1} \sqrt[3]{- 36 a {_C 1}^{2} + 8 x^{3} + 12 \sqrt{a (9 a {_C 1}^{2} - 4 x^{3})}_C 1} - \frac{x^{2}}{3_C 1} \frac{1}{\sqrt[3]{- 36 a {_C 1}^{2} + 8 x^{3} + 12 \sqrt{a (9 a {_C 1}^{2} - 4 x^{3})}_C 1}} + \frac{x}{3_C 1} + \frac{i}{2} \sqrt{3} (\frac{1}{6_C 1} \sqrt[3]{- 36 a {_C 1}^{2} + 8 x^{3} + 12 \sqrt{a (9 a {_C 1}^{2} - 4 x^{3})}_C 1} - \frac{2 x^{2}}{3_C 1} \frac{1}{\sqrt[3]{- 36 a {_C 1}^{2} + 8 x^{3} + 12 \sqrt{a (9 a {_C 1}^{2} - 4 x^{3})}_C 1}}))}^{- 1}}$

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