\[ \boxed { x \left ( {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) \right ) ^{2}-2\,y \left ( x \right ) {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) +a=0} \]
Mathematica: cpu = 1.329169 (sec), leaf count = 11757 \[ \left \{\left \{y(x)\to -\sqrt {\frac {9 a^4 \left (\cosh \left (3 c_1\right )-\sinh \left (3 c_1\right )\right ) x^8}{16 \sqrt [3]{27 a^6 x^{12}-144 a^5 \cosh \left (3 c_1\right ) x^9-144 a^5 \sinh \left (3 c_1\right ) x^9+272 a^4 \cosh \left (6 c_1\right ) x^6+272 a^4 \sinh \left (6 c_1\right ) x^6-256 a^3 \cosh \left (9 c_1\right ) x^3-256 a^3 \sinh \left (9 c_1\right ) x^3+128 a^2 \cosh \left (12 c_1\right )+128 a^2 \sinh \left (12 c_1\right )+64 \sqrt {-a^9 \cosh \left (9 c_1\right ) x^{15}-a^9 \sinh \left (9 c_1\right ) x^{15}+7 a^8 \cosh \left (12 c_1\right ) x^{12}+7 a^8 \sinh \left (12 c_1\right ) x^{12}-19 a^7 \cosh \left (15 c_1\right ) x^9-19 a^7 \sinh \left (15 c_1\right ) x^9+25 a^6 \cosh \left (18 c_1\right ) x^6+25 a^6 \sinh \left (18 c_1\right ) x^6-16 a^5 \cosh \left (21 c_1\right ) x^3-16 a^5 \sinh \left (21 c_1\right ) x^3+4 a^4 \cosh \left (24 c_1\right )+4 a^4 \sinh \left (24 c_1\right )}}}-\frac {2 a^3 x^5}{\sqrt [3]{27 a^6 x^{12}-144 a^5 \cosh \left (3 c_1\right ) x^9-144 a^5 \sinh \left (3 c_1\right ) x^9+272 a^4 \cosh \left (6 c_1\right ) x^6+272 a^4 \sinh \left (6 c_1\right ) x^6-256 a^3 \cosh \left (9 c_1\right ) x^3-256 a^3 \sinh \left (9 c_1\right ) x^3+128 a^2 \cosh \left (12 c_1\right )+128 a^2 \sinh \left (12 c_1\right )+64 \sqrt {-a^9 \cosh \left (9 c_1\right ) x^{15}-a^9 \sinh \left (9 c_1\right ) x^{15}+7 a^8 \cosh \left (12 c_1\right ) x^{12}+7 a^8 \sinh \left (12 c_1\right ) x^{12}-19 a^7 \cosh \left (15 c_1\right ) x^9-19 a^7 \sinh \left (15 c_1\right ) x^9+25 a^6 \cosh \left (18 c_1\right ) x^6+25 a^6 \sinh \left (18 c_1\right ) x^6-16 a^5 \cosh \left (21 c_1\right ) x^3-16 a^5 \sinh \left (21 c_1\right ) x^3+4 a^4 \cosh \left (24 c_1\right )+4 a^4 \sinh \left (24 c_1\right )}}}+\frac {3}{16} a^2 \cosh \left (3 c_1\right ) x^4-\frac {3}{16} a^2 \sinh \left (3 c_1\right ) x^4+\frac {2 a^2 \left (\cosh \left (3 c_1\right )+\sinh \left (3 c_1\right )\right ) x^2}{\sqrt [3]{27 a^6 x^{12}-144 a^5 \cosh \left (3 c_1\right ) x^9-144 a^5 \sinh \left (3 c_1\right ) x^9+272 a^4 \cosh \left (6 c_1\right ) x^6+272 a^4 \sinh \left (6 c_1\right ) x^6-256 a^3 \cosh \left (9 c_1\right ) x^3-256 a^3 \sinh \left (9 c_1\right ) x^3+128 a^2 \cosh \left (12 c_1\right )+128 a^2 \sinh \left (12 c_1\right )+64 \sqrt {-a^9 \cosh \left (9 c_1\right ) x^{15}-a^9 \sinh \left (9 c_1\right ) x^{15}+7 a^8 \cosh \left (12 c_1\right ) x^{12}+7 a^8 \sinh \left (12 c_1\right ) x^{12}-19 a^7 \cosh \left (15 c_1\right ) x^9-19 a^7 \sinh \left (15 c_1\right ) x^9+25 a^6 \cosh \left (18 c_1\right ) x^6+25 a^6 \sinh \left (18 c_1\right ) x^6-16 a^5 \cosh \left (21 c_1\right ) x^3-16 a^5 \sinh \left (21 c_1\right ) x^3+4 a^4 \cosh \left (24 c_1\right )+4 a^4 \sinh \left (24 c_1\right )}}}+a x+\frac {1}{16} \left (\cosh \left (3 c_1\right )-\sinh \left (3 c_1\right )\right ) \sqrt [3]{27 a^6 x^{12}-144 a^5 \cosh \left (3 c_1\right ) x^9-144 a^5 \sinh \left (3 c_1\right ) x^9+272 a^4 \cosh \left (6 c_1\right ) x^6+272 a^4 \sinh \left (6 c_1\right ) x^6-256 a^3 \cosh \left (9 c_1\right ) x^3-256 a^3 \sinh \left (9 c_1\right ) x^3+128 a^2 \cosh \left (12 c_1\right )+128 a^2 \sinh \left (12 c_1\right )+64 \sqrt {-a^9 \cosh \left (9 c_1\right ) x^{15}-a^9 \sinh \left (9 c_1\right ) x^{15}+7 a^8 \cosh \left (12 c_1\right ) x^{12}+7 a^8 \sinh \left (12 c_1\right ) x^{12}-19 a^7 \cosh \left (15 c_1\right ) x^9-19 a^7 \sinh \left (15 c_1\right ) x^9+25 a^6 \cosh \left (18 c_1\right ) x^6+25 a^6 \sinh \left (18 c_1\right ) x^6-16 a^5 \cosh \left (21 c_1\right ) x^3-16 a^5 \sinh \left (21 c_1\right ) x^3+4 a^4 \cosh \left (24 c_1\right )+4 a^4 \sinh \left (24 c_1\right )}}}\right \},\left \{y(x)\to \sqrt {\frac {9 a^4 \left (\cosh \left (3 c_1\right )-\sinh \left (3 c_1\right )\right ) x^8}{16 \sqrt [3]{27 a^6 x^{12}-144 a^5 \cosh \left (3 c_1\right ) x^9-144 a^5 \sinh \left (3 c_1\right ) x^9+272 a^4 \cosh \left (6 c_1\right ) x^6+272 a^4 \sinh \left (6 c_1\right ) x^6-256 a^3 \cosh \left (9 c_1\right ) x^3-256 a^3 \sinh \left (9 c_1\right ) x^3+128 a^2 \cosh \left (12 c_1\right )+128 a^2 \sinh \left (12 c_1\right )+64 \sqrt {-a^9 \cosh \left (9 c_1\right ) x^{15}-a^9 \sinh \left (9 c_1\right ) x^{15}+7 a^8 \cosh \left (12 c_1\right ) x^{12}+7 a^8 \sinh \left (12 c_1\right ) x^{12}-19 a^7 \cosh \left (15 c_1\right ) x^9-19 a^7 \sinh \left (15 c_1\right ) x^9+25 a^6 \cosh \left (18 c_1\right ) x^6+25 a^6 \sinh \left (18 c_1\right ) x^6-16 a^5 \cosh \left (21 c_1\right ) x^3-16 a^5 \sinh \left (21 c_1\right ) x^3+4 a^4 \cosh \left (24 c_1\right )+4 a^4 \sinh \left (24 c_1\right )}}}-\frac {2 a^3 x^5}{\sqrt [3]{27 a^6 x^{12}-144 a^5 \cosh \left (3 c_1\right ) x^9-144 a^5 \sinh \left (3 c_1\right ) x^9+272 a^4 \cosh \left (6 c_1\right ) x^6+272 a^4 \sinh \left (6 c_1\right ) x^6-256 a^3 \cosh \left (9 c_1\right ) x^3-256 a^3 \sinh \left (9 c_1\right ) x^3+128 a^2 \cosh \left (12 c_1\right )+128 a^2 \sinh \left (12 c_1\right )+64 \sqrt {-a^9 \cosh \left (9 c_1\right ) x^{15}-a^9 \sinh \left (9 c_1\right ) x^{15}+7 a^8 \cosh \left (12 c_1\right ) x^{12}+7 a^8 \sinh \left (12 c_1\right ) x^{12}-19 a^7 \cosh \left (15 c_1\right ) x^9-19 a^7 \sinh \left (15 c_1\right ) x^9+25 a^6 \cosh \left (18 c_1\right ) x^6+25 a^6 \sinh \left (18 c_1\right ) x^6-16 a^5 \cosh \left (21 c_1\right ) x^3-16 a^5 \sinh \left (21 c_1\right ) x^3+4 a^4 \cosh \left (24 c_1\right )+4 a^4 \sinh \left (24 c_1\right )}}}+\frac {3}{16} a^2 \cosh \left (3 c_1\right ) x^4-\frac {3}{16} a^2 \sinh \left (3 c_1\right ) x^4+\frac {2 a^2 \left (\cosh \left (3 c_1\right )+\sinh \left (3 c_1\right )\right ) x^2}{\sqrt [3]{27 a^6 x^{12}-144 a^5 \cosh \left (3 c_1\right ) x^9-144 a^5 \sinh \left (3 c_1\right ) x^9+272 a^4 \cosh \left (6 c_1\right ) x^6+272 a^4 \sinh \left (6 c_1\right ) x^6-256 a^3 \cosh \left (9 c_1\right ) x^3-256 a^3 \sinh \left (9 c_1\right ) x^3+128 a^2 \cosh \left (12 c_1\right )+128 a^2 \sinh \left (12 c_1\right )+64 \sqrt {-a^9 \cosh \left (9 c_1\right ) x^{15}-a^9 \sinh \left (9 c_1\right ) x^{15}+7 a^8 \cosh \left (12 c_1\right ) x^{12}+7 a^8 \sinh \left (12 c_1\right ) x^{12}-19 a^7 \cosh \left (15 c_1\right ) x^9-19 a^7 \sinh \left (15 c_1\right ) x^9+25 a^6 \cosh \left (18 c_1\right ) x^6+25 a^6 \sinh \left (18 c_1\right ) x^6-16 a^5 \cosh \left (21 c_1\right ) x^3-16 a^5 \sinh \left (21 c_1\right ) x^3+4 a^4 \cosh \left (24 c_1\right )+4 a^4 \sinh \left (24 c_1\right )}}}+a x+\frac {1}{16} \left (\cosh \left (3 c_1\right )-\sinh \left (3 c_1\right )\right ) \sqrt [3]{27 a^6 x^{12}-144 a^5 \cosh \left (3 c_1\right ) x^9-144 a^5 \sinh \left (3 c_1\right ) x^9+272 a^4 \cosh \left (6 c_1\right ) x^6+272 a^4 \sinh \left (6 c_1\right ) x^6-256 a^3 \cosh \left (9 c_1\right ) x^3-256 a^3 \sinh \left (9 c_1\right ) x^3+128 a^2 \cosh \left (12 c_1\right )+128 a^2 \sinh \left (12 c_1\right )+64 \sqrt {-a^9 \cosh \left (9 c_1\right ) x^{15}-a^9 \sinh \left (9 c_1\right ) x^{15}+7 a^8 \cosh \left (12 c_1\right ) x^{12}+7 a^8 \sinh \left (12 c_1\right ) x^{12}-19 a^7 \cosh \left (15 c_1\right ) x^9-19 a^7 \sinh \left (15 c_1\right ) x^9+25 a^6 \cosh \left (18 c_1\right ) x^6+25 a^6 \sinh \left (18 c_1\right ) x^6-16 a^5 \cosh \left (21 c_1\right ) x^3-16 a^5 \sinh \left (21 c_1\right ) x^3+4 a^4 \cosh \left (24 c_1\right )+4 a^4 \sinh \left (24 c_1\right )}}}\right \},\left \{y(x)\to -\sqrt {\frac {9 i \sqrt {3} a^4 \left (\cosh \left (3 c_1\right )-\sinh \left (3 c_1\right )\right ) x^8}{32 \sqrt [3]{27 a^6 x^{12}-144 a^5 \cosh \left (3 c_1\right ) x^9-144 a^5 \sinh \left (3 c_1\right ) x^9+272 a^4 \cosh \left (6 c_1\right ) x^6+272 a^4 \sinh \left (6 c_1\right ) x^6-256 a^3 \cosh \left (9 c_1\right ) x^3-256 a^3 \sinh \left (9 c_1\right ) x^3+128 a^2 \cosh \left (12 c_1\right )+128 a^2 \sinh \left (12 c_1\right )+64 \sqrt {-a^9 \cosh \left (9 c_1\right ) x^{15}-a^9 \sinh \left (9 c_1\right ) x^{15}+7 a^8 \cosh \left (12 c_1\right ) x^{12}+7 a^8 \sinh \left (12 c_1\right ) x^{12}-19 a^7 \cosh \left (15 c_1\right ) x^9-19 a^7 \sinh \left (15 c_1\right ) x^9+25 a^6 \cosh \left (18 c_1\right ) x^6+25 a^6 \sinh \left (18 c_1\right ) x^6-16 a^5 \cosh \left (21 c_1\right ) x^3-16 a^5 \sinh \left (21 c_1\right ) x^3+4 a^4 \cosh \left (24 c_1\right )+4 a^4 \sinh \left (24 c_1\right )}}}-\frac {9 a^4 \left (\cosh \left (3 c_1\right )-\sinh \left (3 c_1\right )\right ) x^8}{32 \sqrt [3]{27 a^6 x^{12}-144 a^5 \cosh \left (3 c_1\right ) x^9-144 a^5 \sinh \left (3 c_1\right ) x^9+272 a^4 \cosh \left (6 c_1\right ) x^6+272 a^4 \sinh \left (6 c_1\right ) x^6-256 a^3 \cosh \left (9 c_1\right ) x^3-256 a^3 \sinh \left (9 c_1\right ) x^3+128 a^2 \cosh \left (12 c_1\right )+128 a^2 \sinh \left (12 c_1\right )+64 \sqrt {-a^9 \cosh \left (9 c_1\right ) x^{15}-a^9 \sinh \left (9 c_1\right ) x^{15}+7 a^8 \cosh \left (12 c_1\right ) x^{12}+7 a^8 \sinh \left (12 c_1\right ) x^{12}-19 a^7 \cosh \left (15 c_1\right ) x^9-19 a^7 \sinh \left (15 c_1\right ) x^9+25 a^6 \cosh \left (18 c_1\right ) x^6+25 a^6 \sinh \left (18 c_1\right ) x^6-16 a^5 \cosh \left (21 c_1\right ) x^3-16 a^5 \sinh \left (21 c_1\right ) x^3+4 a^4 \cosh \left (24 c_1\right )+4 a^4 \sinh \left (24 c_1\right )}}}-\frac {i \sqrt {3} a^3 x^5}{\sqrt [3]{27 a^6 x^{12}-144 a^5 \cosh \left (3 c_1\right ) x^9-144 a^5 \sinh \left (3 c_1\right ) x^9+272 a^4 \cosh \left (6 c_1\right ) x^6+272 a^4 \sinh \left (6 c_1\right ) x^6-256 a^3 \cosh \left (9 c_1\right ) x^3-256 a^3 \sinh \left (9 c_1\right ) x^3+128 a^2 \cosh \left (12 c_1\right )+128 a^2 \sinh \left (12 c_1\right )+64 \sqrt {-a^9 \cosh \left (9 c_1\right ) x^{15}-a^9 \sinh \left (9 c_1\right ) x^{15}+7 a^8 \cosh \left (12 c_1\right ) x^{12}+7 a^8 \sinh \left (12 c_1\right ) x^{12}-19 a^7 \cosh \left (15 c_1\right ) x^9-19 a^7 \sinh \left (15 c_1\right ) x^9+25 a^6 \cosh \left (18 c_1\right ) x^6+25 a^6 \sinh \left (18 c_1\right ) x^6-16 a^5 \cosh \left (21 c_1\right ) x^3-16 a^5 \sinh \left (21 c_1\right ) x^3+4 a^4 \cosh \left (24 c_1\right )+4 a^4 \sinh \left (24 c_1\right )}}}+\frac {a^3 x^5}{\sqrt [3]{27 a^6 x^{12}-144 a^5 \cosh \left (3 c_1\right ) x^9-144 a^5 \sinh \left (3 c_1\right ) x^9+272 a^4 \cosh \left (6 c_1\right ) x^6+272 a^4 \sinh \left (6 c_1\right ) x^6-256 a^3 \cosh \left (9 c_1\right ) x^3-256 a^3 \sinh \left (9 c_1\right ) x^3+128 a^2 \cosh \left (12 c_1\right )+128 a^2 \sinh \left (12 c_1\right )+64 \sqrt {-a^9 \cosh \left (9 c_1\right ) x^{15}-a^9 \sinh \left (9 c_1\right ) x^{15}+7 a^8 \cosh \left (12 c_1\right ) x^{12}+7 a^8 \sinh \left (12 c_1\right ) x^{12}-19 a^7 \cosh \left (15 c_1\right ) x^9-19 a^7 \sinh \left (15 c_1\right ) x^9+25 a^6 \cosh \left (18 c_1\right ) x^6+25 a^6 \sinh \left (18 c_1\right ) x^6-16 a^5 \cosh \left (21 c_1\right ) x^3-16 a^5 \sinh \left (21 c_1\right ) x^3+4 a^4 \cosh \left (24 c_1\right )+4 a^4 \sinh \left (24 c_1\right )}}}+\frac {3}{16} a^2 \cosh \left (3 c_1\right ) x^4-\frac {3}{16} a^2 \sinh \left (3 c_1\right ) x^4+\frac {i \sqrt {3} a^2 \left (\cosh \left (3 c_1\right )+\sinh \left (3 c_1\right )\right ) x^2}{\sqrt [3]{27 a^6 x^{12}-144 a^5 \cosh \left (3 c_1\right ) x^9-144 a^5 \sinh \left (3 c_1\right ) x^9+272 a^4 \cosh \left (6 c_1\right ) x^6+272 a^4 \sinh \left (6 c_1\right ) x^6-256 a^3 \cosh \left (9 c_1\right ) x^3-256 a^3 \sinh \left (9 c_1\right ) x^3+128 a^2 \cosh \left (12 c_1\right )+128 a^2 \sinh \left (12 c_1\right )+64 \sqrt {-a^9 \cosh \left (9 c_1\right ) x^{15}-a^9 \sinh \left (9 c_1\right ) x^{15}+7 a^8 \cosh \left (12 c_1\right ) x^{12}+7 a^8 \sinh \left (12 c_1\right ) x^{12}-19 a^7 \cosh \left (15 c_1\right ) x^9-19 a^7 \sinh \left (15 c_1\right ) x^9+25 a^6 \cosh \left (18 c_1\right ) x^6+25 a^6 \sinh \left (18 c_1\right ) x^6-16 a^5 \cosh \left (21 c_1\right ) x^3-16 a^5 \sinh \left (21 c_1\right ) x^3+4 a^4 \cosh \left (24 c_1\right )+4 a^4 \sinh \left (24 c_1\right )}}}-\frac {a^2 \left (\cosh \left (3 c_1\right )+\sinh \left (3 c_1\right )\right ) x^2}{\sqrt [3]{27 a^6 x^{12}-144 a^5 \cosh \left (3 c_1\right ) x^9-144 a^5 \sinh \left (3 c_1\right ) x^9+272 a^4 \cosh \left (6 c_1\right ) x^6+272 a^4 \sinh \left (6 c_1\right ) x^6-256 a^3 \cosh \left (9 c_1\right ) x^3-256 a^3 \sinh \left (9 c_1\right ) x^3+128 a^2 \cosh \left (12 c_1\right )+128 a^2 \sinh \left (12 c_1\right )+64 \sqrt {-a^9 \cosh \left (9 c_1\right ) x^{15}-a^9 \sinh \left (9 c_1\right ) x^{15}+7 a^8 \cosh \left (12 c_1\right ) x^{12}+7 a^8 \sinh \left (12 c_1\right ) x^{12}-19 a^7 \cosh \left (15 c_1\right ) x^9-19 a^7 \sinh \left (15 c_1\right ) x^9+25 a^6 \cosh \left (18 c_1\right ) x^6+25 a^6 \sinh \left (18 c_1\right ) x^6-16 a^5 \cosh \left (21 c_1\right ) x^3-16 a^5 \sinh \left (21 c_1\right ) x^3+4 a^4 \cosh \left (24 c_1\right )+4 a^4 \sinh \left (24 c_1\right )}}}+a x-\frac {1}{32} i \sqrt {3} \left (\cosh \left (3 c_1\right )-\sinh \left (3 c_1\right )\right ) \sqrt [3]{27 a^6 x^{12}-144 a^5 \cosh \left (3 c_1\right ) x^9-144 a^5 \sinh \left (3 c_1\right ) x^9+272 a^4 \cosh \left (6 c_1\right ) x^6+272 a^4 \sinh \left (6 c_1\right ) x^6-256 a^3 \cosh \left (9 c_1\right ) x^3-256 a^3 \sinh \left (9 c_1\right ) x^3+128 a^2 \cosh \left (12 c_1\right )+128 a^2 \sinh \left (12 c_1\right )+64 \sqrt {-a^9 \cosh \left (9 c_1\right ) x^{15}-a^9 \sinh \left (9 c_1\right ) x^{15}+7 a^8 \cosh \left (12 c_1\right ) x^{12}+7 a^8 \sinh \left (12 c_1\right ) x^{12}-19 a^7 \cosh \left (15 c_1\right ) x^9-19 a^7 \sinh \left (15 c_1\right ) x^9+25 a^6 \cosh \left (18 c_1\right ) x^6+25 a^6 \sinh \left (18 c_1\right ) x^6-16 a^5 \cosh \left (21 c_1\right ) x^3-16 a^5 \sinh \left (21 c_1\right ) x^3+4 a^4 \cosh \left (24 c_1\right )+4 a^4 \sinh \left (24 c_1\right )}}-\frac {1}{32} \left (\cosh \left (3 c_1\right )-\sinh \left (3 c_1\right )\right ) \sqrt [3]{27 a^6 x^{12}-144 a^5 \cosh \left (3 c_1\right ) x^9-144 a^5 \sinh \left (3 c_1\right ) x^9+272 a^4 \cosh \left (6 c_1\right ) x^6+272 a^4 \sinh \left (6 c_1\right ) x^6-256 a^3 \cosh \left (9 c_1\right ) x^3-256 a^3 \sinh \left (9 c_1\right ) x^3+128 a^2 \cosh \left (12 c_1\right )+128 a^2 \sinh \left (12 c_1\right )+64 \sqrt {-a^9 \cosh \left (9 c_1\right ) x^{15}-a^9 \sinh \left (9 c_1\right ) x^{15}+7 a^8 \cosh \left (12 c_1\right ) x^{12}+7 a^8 \sinh \left (12 c_1\right ) x^{12}-19 a^7 \cosh \left (15 c_1\right ) x^9-19 a^7 \sinh \left (15 c_1\right ) x^9+25 a^6 \cosh \left (18 c_1\right ) x^6+25 a^6 \sinh \left (18 c_1\right ) x^6-16 a^5 \cosh \left (21 c_1\right ) x^3-16 a^5 \sinh \left (21 c_1\right ) x^3+4 a^4 \cosh \left (24 c_1\right )+4 a^4 \sinh \left (24 c_1\right )}}}\right \},\left \{y(x)\to \sqrt {\frac {9 i \sqrt {3} a^4 \left (\cosh \left (3 c_1\right )-\sinh \left (3 c_1\right )\right ) x^8}{32 \sqrt [3]{27 a^6 x^{12}-144 a^5 \cosh \left (3 c_1\right ) x^9-144 a^5 \sinh \left (3 c_1\right ) x^9+272 a^4 \cosh \left (6 c_1\right ) x^6+272 a^4 \sinh \left (6 c_1\right ) x^6-256 a^3 \cosh \left (9 c_1\right ) x^3-256 a^3 \sinh \left (9 c_1\right ) x^3+128 a^2 \cosh \left (12 c_1\right )+128 a^2 \sinh \left (12 c_1\right )+64 \sqrt {-a^9 \cosh \left (9 c_1\right ) x^{15}-a^9 \sinh \left (9 c_1\right ) x^{15}+7 a^8 \cosh \left (12 c_1\right ) x^{12}+7 a^8 \sinh \left (12 c_1\right ) x^{12}-19 a^7 \cosh \left (15 c_1\right ) x^9-19 a^7 \sinh \left (15 c_1\right ) x^9+25 a^6 \cosh \left (18 c_1\right ) x^6+25 a^6 \sinh \left (18 c_1\right ) x^6-16 a^5 \cosh \left (21 c_1\right ) x^3-16 a^5 \sinh \left (21 c_1\right ) x^3+4 a^4 \cosh \left (24 c_1\right )+4 a^4 \sinh \left (24 c_1\right )}}}-\frac {9 a^4 \left (\cosh \left (3 c_1\right )-\sinh \left (3 c_1\right )\right ) x^8}{32 \sqrt [3]{27 a^6 x^{12}-144 a^5 \cosh \left (3 c_1\right ) x^9-144 a^5 \sinh \left (3 c_1\right ) x^9+272 a^4 \cosh \left (6 c_1\right ) x^6+272 a^4 \sinh \left (6 c_1\right ) x^6-256 a^3 \cosh \left (9 c_1\right ) x^3-256 a^3 \sinh \left (9 c_1\right ) x^3+128 a^2 \cosh \left (12 c_1\right )+128 a^2 \sinh \left (12 c_1\right )+64 \sqrt {-a^9 \cosh \left (9 c_1\right ) x^{15}-a^9 \sinh \left (9 c_1\right ) x^{15}+7 a^8 \cosh \left (12 c_1\right ) x^{12}+7 a^8 \sinh \left (12 c_1\right ) x^{12}-19 a^7 \cosh \left (15 c_1\right ) x^9-19 a^7 \sinh \left (15 c_1\right ) x^9+25 a^6 \cosh \left (18 c_1\right ) x^6+25 a^6 \sinh \left (18 c_1\right ) x^6-16 a^5 \cosh \left (21 c_1\right ) x^3-16 a^5 \sinh \left (21 c_1\right ) x^3+4 a^4 \cosh \left (24 c_1\right )+4 a^4 \sinh \left (24 c_1\right )}}}-\frac {i \sqrt {3} a^3 x^5}{\sqrt [3]{27 a^6 x^{12}-144 a^5 \cosh \left (3 c_1\right ) x^9-144 a^5 \sinh \left (3 c_1\right ) x^9+272 a^4 \cosh \left (6 c_1\right ) x^6+272 a^4 \sinh \left (6 c_1\right ) x^6-256 a^3 \cosh \left (9 c_1\right ) x^3-256 a^3 \sinh \left (9 c_1\right ) x^3+128 a^2 \cosh \left (12 c_1\right )+128 a^2 \sinh \left (12 c_1\right )+64 \sqrt {-a^9 \cosh \left (9 c_1\right ) x^{15}-a^9 \sinh \left (9 c_1\right ) x^{15}+7 a^8 \cosh \left (12 c_1\right ) x^{12}+7 a^8 \sinh \left (12 c_1\right ) x^{12}-19 a^7 \cosh \left (15 c_1\right ) x^9-19 a^7 \sinh \left (15 c_1\right ) x^9+25 a^6 \cosh \left (18 c_1\right ) x^6+25 a^6 \sinh \left (18 c_1\right ) x^6-16 a^5 \cosh \left (21 c_1\right ) x^3-16 a^5 \sinh \left (21 c_1\right ) x^3+4 a^4 \cosh \left (24 c_1\right )+4 a^4 \sinh \left (24 c_1\right )}}}+\frac {a^3 x^5}{\sqrt [3]{27 a^6 x^{12}-144 a^5 \cosh \left (3 c_1\right ) x^9-144 a^5 \sinh \left (3 c_1\right ) x^9+272 a^4 \cosh \left (6 c_1\right ) x^6+272 a^4 \sinh \left (6 c_1\right ) x^6-256 a^3 \cosh \left (9 c_1\right ) x^3-256 a^3 \sinh \left (9 c_1\right ) x^3+128 a^2 \cosh \left (12 c_1\right )+128 a^2 \sinh \left (12 c_1\right )+64 \sqrt {-a^9 \cosh \left (9 c_1\right ) x^{15}-a^9 \sinh \left (9 c_1\right ) x^{15}+7 a^8 \cosh \left (12 c_1\right ) x^{12}+7 a^8 \sinh \left (12 c_1\right ) x^{12}-19 a^7 \cosh \left (15 c_1\right ) x^9-19 a^7 \sinh \left (15 c_1\right ) x^9+25 a^6 \cosh \left (18 c_1\right ) x^6+25 a^6 \sinh \left (18 c_1\right ) x^6-16 a^5 \cosh \left (21 c_1\right ) x^3-16 a^5 \sinh \left (21 c_1\right ) x^3+4 a^4 \cosh \left (24 c_1\right )+4 a^4 \sinh \left (24 c_1\right )}}}+\frac {3}{16} a^2 \cosh \left (3 c_1\right ) x^4-\frac {3}{16} a^2 \sinh \left (3 c_1\right ) x^4+\frac {i \sqrt {3} a^2 \left (\cosh \left (3 c_1\right )+\sinh \left (3 c_1\right )\right ) x^2}{\sqrt [3]{27 a^6 x^{12}-144 a^5 \cosh \left (3 c_1\right ) x^9-144 a^5 \sinh \left (3 c_1\right ) x^9+272 a^4 \cosh \left (6 c_1\right ) x^6+272 a^4 \sinh \left (6 c_1\right ) x^6-256 a^3 \cosh \left (9 c_1\right ) x^3-256 a^3 \sinh \left (9 c_1\right ) x^3+128 a^2 \cosh \left (12 c_1\right )+128 a^2 \sinh \left (12 c_1\right )+64 \sqrt {-a^9 \cosh \left (9 c_1\right ) x^{15}-a^9 \sinh \left (9 c_1\right ) x^{15}+7 a^8 \cosh \left (12 c_1\right ) x^{12}+7 a^8 \sinh \left (12 c_1\right ) x^{12}-19 a^7 \cosh \left (15 c_1\right ) x^9-19 a^7 \sinh \left (15 c_1\right ) x^9+25 a^6 \cosh \left (18 c_1\right ) x^6+25 a^6 \sinh \left (18 c_1\right ) x^6-16 a^5 \cosh \left (21 c_1\right ) x^3-16 a^5 \sinh \left (21 c_1\right ) x^3+4 a^4 \cosh \left (24 c_1\right )+4 a^4 \sinh \left (24 c_1\right )}}}-\frac {a^2 \left (\cosh \left (3 c_1\right )+\sinh \left (3 c_1\right )\right ) x^2}{\sqrt [3]{27 a^6 x^{12}-144 a^5 \cosh \left (3 c_1\right ) x^9-144 a^5 \sinh \left (3 c_1\right ) x^9+272 a^4 \cosh \left (6 c_1\right ) x^6+272 a^4 \sinh \left (6 c_1\right ) x^6-256 a^3 \cosh \left (9 c_1\right ) x^3-256 a^3 \sinh \left (9 c_1\right ) x^3+128 a^2 \cosh \left (12 c_1\right )+128 a^2 \sinh \left (12 c_1\right )+64 \sqrt {-a^9 \cosh \left (9 c_1\right ) x^{15}-a^9 \sinh \left (9 c_1\right ) x^{15}+7 a^8 \cosh \left (12 c_1\right ) x^{12}+7 a^8 \sinh \left (12 c_1\right ) x^{12}-19 a^7 \cosh \left (15 c_1\right ) x^9-19 a^7 \sinh \left (15 c_1\right ) x^9+25 a^6 \cosh \left (18 c_1\right ) x^6+25 a^6 \sinh \left (18 c_1\right ) x^6-16 a^5 \cosh \left (21 c_1\right ) x^3-16 a^5 \sinh \left (21 c_1\right ) x^3+4 a^4 \cosh \left (24 c_1\right )+4 a^4 \sinh \left (24 c_1\right )}}}+a x-\frac {1}{32} i \sqrt {3} \left (\cosh \left (3 c_1\right )-\sinh \left (3 c_1\right )\right ) \sqrt [3]{27 a^6 x^{12}-144 a^5 \cosh \left (3 c_1\right ) x^9-144 a^5 \sinh \left (3 c_1\right ) x^9+272 a^4 \cosh \left (6 c_1\right ) x^6+272 a^4 \sinh \left (6 c_1\right ) x^6-256 a^3 \cosh \left (9 c_1\right ) x^3-256 a^3 \sinh \left (9 c_1\right ) x^3+128 a^2 \cosh \left (12 c_1\right )+128 a^2 \sinh \left (12 c_1\right )+64 \sqrt {-a^9 \cosh \left (9 c_1\right ) x^{15}-a^9 \sinh \left (9 c_1\right ) x^{15}+7 a^8 \cosh \left (12 c_1\right ) x^{12}+7 a^8 \sinh \left (12 c_1\right ) x^{12}-19 a^7 \cosh \left (15 c_1\right ) x^9-19 a^7 \sinh \left (15 c_1\right ) x^9+25 a^6 \cosh \left (18 c_1\right ) x^6+25 a^6 \sinh \left (18 c_1\right ) x^6-16 a^5 \cosh \left (21 c_1\right ) x^3-16 a^5 \sinh \left (21 c_1\right ) x^3+4 a^4 \cosh \left (24 c_1\right )+4 a^4 \sinh \left (24 c_1\right )}}-\frac {1}{32} \left (\cosh \left (3 c_1\right )-\sinh \left (3 c_1\right )\right ) \sqrt [3]{27 a^6 x^{12}-144 a^5 \cosh \left (3 c_1\right ) x^9-144 a^5 \sinh \left (3 c_1\right ) x^9+272 a^4 \cosh \left (6 c_1\right ) x^6+272 a^4 \sinh \left (6 c_1\right ) x^6-256 a^3 \cosh \left (9 c_1\right ) x^3-256 a^3 \sinh \left (9 c_1\right ) x^3+128 a^2 \cosh \left (12 c_1\right )+128 a^2 \sinh \left (12 c_1\right )+64 \sqrt {-a^9 \cosh \left (9 c_1\right ) x^{15}-a^9 \sinh \left (9 c_1\right ) x^{15}+7 a^8 \cosh \left (12 c_1\right ) x^{12}+7 a^8 \sinh \left (12 c_1\right ) x^{12}-19 a^7 \cosh \left (15 c_1\right ) x^9-19 a^7 \sinh \left (15 c_1\right ) x^9+25 a^6 \cosh \left (18 c_1\right ) x^6+25 a^6 \sinh \left (18 c_1\right ) x^6-16 a^5 \cosh \left (21 c_1\right ) x^3-16 a^5 \sinh \left (21 c_1\right ) x^3+4 a^4 \cosh \left (24 c_1\right )+4 a^4 \sinh \left (24 c_1\right )}}}\right \},\left \{y(x)\to -\sqrt {-\frac {9 i \sqrt {3} a^4 \left (\cosh \left (3 c_1\right )-\sinh \left (3 c_1\right )\right ) x^8}{32 \sqrt [3]{27 a^6 x^{12}-144 a^5 \cosh \left (3 c_1\right ) x^9-144 a^5 \sinh \left (3 c_1\right ) x^9+272 a^4 \cosh \left (6 c_1\right ) x^6+272 a^4 \sinh \left (6 c_1\right ) x^6-256 a^3 \cosh \left (9 c_1\right ) x^3-256 a^3 \sinh \left (9 c_1\right ) x^3+128 a^2 \cosh \left (12 c_1\right )+128 a^2 \sinh \left (12 c_1\right )+64 \sqrt {-a^9 \cosh \left (9 c_1\right ) x^{15}-a^9 \sinh \left (9 c_1\right ) x^{15}+7 a^8 \cosh \left (12 c_1\right ) x^{12}+7 a^8 \sinh \left (12 c_1\right ) x^{12}-19 a^7 \cosh \left (15 c_1\right ) x^9-19 a^7 \sinh \left (15 c_1\right ) x^9+25 a^6 \cosh \left (18 c_1\right ) x^6+25 a^6 \sinh \left (18 c_1\right ) x^6-16 a^5 \cosh \left (21 c_1\right ) x^3-16 a^5 \sinh \left (21 c_1\right ) x^3+4 a^4 \cosh \left (24 c_1\right )+4 a^4 \sinh \left (24 c_1\right )}}}-\frac {9 a^4 \left (\cosh \left (3 c_1\right )-\sinh \left (3 c_1\right )\right ) x^8}{32 \sqrt [3]{27 a^6 x^{12}-144 a^5 \cosh \left (3 c_1\right ) x^9-144 a^5 \sinh \left (3 c_1\right ) x^9+272 a^4 \cosh \left (6 c_1\right ) x^6+272 a^4 \sinh \left (6 c_1\right ) x^6-256 a^3 \cosh \left (9 c_1\right ) x^3-256 a^3 \sinh \left (9 c_1\right ) x^3+128 a^2 \cosh \left (12 c_1\right )+128 a^2 \sinh \left (12 c_1\right )+64 \sqrt {-a^9 \cosh \left (9 c_1\right ) x^{15}-a^9 \sinh \left (9 c_1\right ) x^{15}+7 a^8 \cosh \left (12 c_1\right ) x^{12}+7 a^8 \sinh \left (12 c_1\right ) x^{12}-19 a^7 \cosh \left (15 c_1\right ) x^9-19 a^7 \sinh \left (15 c_1\right ) x^9+25 a^6 \cosh \left (18 c_1\right ) x^6+25 a^6 \sinh \left (18 c_1\right ) x^6-16 a^5 \cosh \left (21 c_1\right ) x^3-16 a^5 \sinh \left (21 c_1\right ) x^3+4 a^4 \cosh \left (24 c_1\right )+4 a^4 \sinh \left (24 c_1\right )}}}+\frac {i \sqrt {3} a^3 x^5}{\sqrt [3]{27 a^6 x^{12}-144 a^5 \cosh \left (3 c_1\right ) x^9-144 a^5 \sinh \left (3 c_1\right ) x^9+272 a^4 \cosh \left (6 c_1\right ) x^6+272 a^4 \sinh \left (6 c_1\right ) x^6-256 a^3 \cosh \left (9 c_1\right ) x^3-256 a^3 \sinh \left (9 c_1\right ) x^3+128 a^2 \cosh \left (12 c_1\right )+128 a^2 \sinh \left (12 c_1\right )+64 \sqrt {-a^9 \cosh \left (9 c_1\right ) x^{15}-a^9 \sinh \left (9 c_1\right ) x^{15}+7 a^8 \cosh \left (12 c_1\right ) x^{12}+7 a^8 \sinh \left (12 c_1\right ) x^{12}-19 a^7 \cosh \left (15 c_1\right ) x^9-19 a^7 \sinh \left (15 c_1\right ) x^9+25 a^6 \cosh \left (18 c_1\right ) x^6+25 a^6 \sinh \left (18 c_1\right ) x^6-16 a^5 \cosh \left (21 c_1\right ) x^3-16 a^5 \sinh \left (21 c_1\right ) x^3+4 a^4 \cosh \left (24 c_1\right )+4 a^4 \sinh \left (24 c_1\right )}}}+\frac {a^3 x^5}{\sqrt [3]{27 a^6 x^{12}-144 a^5 \cosh \left (3 c_1\right ) x^9-144 a^5 \sinh \left (3 c_1\right ) x^9+272 a^4 \cosh \left (6 c_1\right ) x^6+272 a^4 \sinh \left (6 c_1\right ) x^6-256 a^3 \cosh \left (9 c_1\right ) x^3-256 a^3 \sinh \left (9 c_1\right ) x^3+128 a^2 \cosh \left (12 c_1\right )+128 a^2 \sinh \left (12 c_1\right )+64 \sqrt {-a^9 \cosh \left (9 c_1\right ) x^{15}-a^9 \sinh \left (9 c_1\right ) x^{15}+7 a^8 \cosh \left (12 c_1\right ) x^{12}+7 a^8 \sinh \left (12 c_1\right ) x^{12}-19 a^7 \cosh \left (15 c_1\right ) x^9-19 a^7 \sinh \left (15 c_1\right ) x^9+25 a^6 \cosh \left (18 c_1\right ) x^6+25 a^6 \sinh \left (18 c_1\right ) x^6-16 a^5 \cosh \left (21 c_1\right ) x^3-16 a^5 \sinh \left (21 c_1\right ) x^3+4 a^4 \cosh \left (24 c_1\right )+4 a^4 \sinh \left (24 c_1\right )}}}+\frac {3}{16} a^2 \cosh \left (3 c_1\right ) x^4-\frac {3}{16} a^2 \sinh \left (3 c_1\right ) x^4-\frac {i \sqrt {3} a^2 \left (\cosh \left (3 c_1\right )+\sinh \left (3 c_1\right )\right ) x^2}{\sqrt [3]{27 a^6 x^{12}-144 a^5 \cosh \left (3 c_1\right ) x^9-144 a^5 \sinh \left (3 c_1\right ) x^9+272 a^4 \cosh \left (6 c_1\right ) x^6+272 a^4 \sinh \left (6 c_1\right ) x^6-256 a^3 \cosh \left (9 c_1\right ) x^3-256 a^3 \sinh \left (9 c_1\right ) x^3+128 a^2 \cosh \left (12 c_1\right )+128 a^2 \sinh \left (12 c_1\right )+64 \sqrt {-a^9 \cosh \left (9 c_1\right ) x^{15}-a^9 \sinh \left (9 c_1\right ) x^{15}+7 a^8 \cosh \left (12 c_1\right ) x^{12}+7 a^8 \sinh \left (12 c_1\right ) x^{12}-19 a^7 \cosh \left (15 c_1\right ) x^9-19 a^7 \sinh \left (15 c_1\right ) x^9+25 a^6 \cosh \left (18 c_1\right ) x^6+25 a^6 \sinh \left (18 c_1\right ) x^6-16 a^5 \cosh \left (21 c_1\right ) x^3-16 a^5 \sinh \left (21 c_1\right ) x^3+4 a^4 \cosh \left (24 c_1\right )+4 a^4 \sinh \left (24 c_1\right )}}}-\frac {a^2 \left (\cosh \left (3 c_1\right )+\sinh \left (3 c_1\right )\right ) x^2}{\sqrt [3]{27 a^6 x^{12}-144 a^5 \cosh \left (3 c_1\right ) x^9-144 a^5 \sinh \left (3 c_1\right ) x^9+272 a^4 \cosh \left (6 c_1\right ) x^6+272 a^4 \sinh \left (6 c_1\right ) x^6-256 a^3 \cosh \left (9 c_1\right ) x^3-256 a^3 \sinh \left (9 c_1\right ) x^3+128 a^2 \cosh \left (12 c_1\right )+128 a^2 \sinh \left (12 c_1\right )+64 \sqrt {-a^9 \cosh \left (9 c_1\right ) x^{15}-a^9 \sinh \left (9 c_1\right ) x^{15}+7 a^8 \cosh \left (12 c_1\right ) x^{12}+7 a^8 \sinh \left (12 c_1\right ) x^{12}-19 a^7 \cosh \left (15 c_1\right ) x^9-19 a^7 \sinh \left (15 c_1\right ) x^9+25 a^6 \cosh \left (18 c_1\right ) x^6+25 a^6 \sinh \left (18 c_1\right ) x^6-16 a^5 \cosh \left (21 c_1\right ) x^3-16 a^5 \sinh \left (21 c_1\right ) x^3+4 a^4 \cosh \left (24 c_1\right )+4 a^4 \sinh \left (24 c_1\right )}}}+a x+\frac {1}{32} i \sqrt {3} \left (\cosh \left (3 c_1\right )-\sinh \left (3 c_1\right )\right ) \sqrt [3]{27 a^6 x^{12}-144 a^5 \cosh \left (3 c_1\right ) x^9-144 a^5 \sinh \left (3 c_1\right ) x^9+272 a^4 \cosh \left (6 c_1\right ) x^6+272 a^4 \sinh \left (6 c_1\right ) x^6-256 a^3 \cosh \left (9 c_1\right ) x^3-256 a^3 \sinh \left (9 c_1\right ) x^3+128 a^2 \cosh \left (12 c_1\right )+128 a^2 \sinh \left (12 c_1\right )+64 \sqrt {-a^9 \cosh \left (9 c_1\right ) x^{15}-a^9 \sinh \left (9 c_1\right ) x^{15}+7 a^8 \cosh \left (12 c_1\right ) x^{12}+7 a^8 \sinh \left (12 c_1\right ) x^{12}-19 a^7 \cosh \left (15 c_1\right ) x^9-19 a^7 \sinh \left (15 c_1\right ) x^9+25 a^6 \cosh \left (18 c_1\right ) x^6+25 a^6 \sinh \left (18 c_1\right ) x^6-16 a^5 \cosh \left (21 c_1\right ) x^3-16 a^5 \sinh \left (21 c_1\right ) x^3+4 a^4 \cosh \left (24 c_1\right )+4 a^4 \sinh \left (24 c_1\right )}}-\frac {1}{32} \left (\cosh \left (3 c_1\right )-\sinh \left (3 c_1\right )\right ) \sqrt [3]{27 a^6 x^{12}-144 a^5 \cosh \left (3 c_1\right ) x^9-144 a^5 \sinh \left (3 c_1\right ) x^9+272 a^4 \cosh \left (6 c_1\right ) x^6+272 a^4 \sinh \left (6 c_1\right ) x^6-256 a^3 \cosh \left (9 c_1\right ) x^3-256 a^3 \sinh \left (9 c_1\right ) x^3+128 a^2 \cosh \left (12 c_1\right )+128 a^2 \sinh \left (12 c_1\right )+64 \sqrt {-a^9 \cosh \left (9 c_1\right ) x^{15}-a^9 \sinh \left (9 c_1\right ) x^{15}+7 a^8 \cosh \left (12 c_1\right ) x^{12}+7 a^8 \sinh \left (12 c_1\right ) x^{12}-19 a^7 \cosh \left (15 c_1\right ) x^9-19 a^7 \sinh \left (15 c_1\right ) x^9+25 a^6 \cosh \left (18 c_1\right ) x^6+25 a^6 \sinh \left (18 c_1\right ) x^6-16 a^5 \cosh \left (21 c_1\right ) x^3-16 a^5 \sinh \left (21 c_1\right ) x^3+4 a^4 \cosh \left (24 c_1\right )+4 a^4 \sinh \left (24 c_1\right )}}}\right \},\left \{y(x)\to \sqrt {-\frac {9 i \sqrt {3} a^4 \left (\cosh \left (3 c_1\right )-\sinh \left (3 c_1\right )\right ) x^8}{32 \sqrt [3]{27 a^6 x^{12}-144 a^5 \cosh \left (3 c_1\right ) x^9-144 a^5 \sinh \left (3 c_1\right ) x^9+272 a^4 \cosh \left (6 c_1\right ) x^6+272 a^4 \sinh \left (6 c_1\right ) x^6-256 a^3 \cosh \left (9 c_1\right ) x^3-256 a^3 \sinh \left (9 c_1\right ) x^3+128 a^2 \cosh \left (12 c_1\right )+128 a^2 \sinh \left (12 c_1\right )+64 \sqrt {-a^9 \cosh \left (9 c_1\right ) x^{15}-a^9 \sinh \left (9 c_1\right ) x^{15}+7 a^8 \cosh \left (12 c_1\right ) x^{12}+7 a^8 \sinh \left (12 c_1\right ) x^{12}-19 a^7 \cosh \left (15 c_1\right ) x^9-19 a^7 \sinh \left (15 c_1\right ) x^9+25 a^6 \cosh \left (18 c_1\right ) x^6+25 a^6 \sinh \left (18 c_1\right ) x^6-16 a^5 \cosh \left (21 c_1\right ) x^3-16 a^5 \sinh \left (21 c_1\right ) x^3+4 a^4 \cosh \left (24 c_1\right )+4 a^4 \sinh \left (24 c_1\right )}}}-\frac {9 a^4 \left (\cosh \left (3 c_1\right )-\sinh \left (3 c_1\right )\right ) x^8}{32 \sqrt [3]{27 a^6 x^{12}-144 a^5 \cosh \left (3 c_1\right ) x^9-144 a^5 \sinh \left (3 c_1\right ) x^9+272 a^4 \cosh \left (6 c_1\right ) x^6+272 a^4 \sinh \left (6 c_1\right ) x^6-256 a^3 \cosh \left (9 c_1\right ) x^3-256 a^3 \sinh \left (9 c_1\right ) x^3+128 a^2 \cosh \left (12 c_1\right )+128 a^2 \sinh \left (12 c_1\right )+64 \sqrt {-a^9 \cosh \left (9 c_1\right ) x^{15}-a^9 \sinh \left (9 c_1\right ) x^{15}+7 a^8 \cosh \left (12 c_1\right ) x^{12}+7 a^8 \sinh \left (12 c_1\right ) x^{12}-19 a^7 \cosh \left (15 c_1\right ) x^9-19 a^7 \sinh \left (15 c_1\right ) x^9+25 a^6 \cosh \left (18 c_1\right ) x^6+25 a^6 \sinh \left (18 c_1\right ) x^6-16 a^5 \cosh \left (21 c_1\right ) x^3-16 a^5 \sinh \left (21 c_1\right ) x^3+4 a^4 \cosh \left (24 c_1\right )+4 a^4 \sinh \left (24 c_1\right )}}}+\frac {i \sqrt {3} a^3 x^5}{\sqrt [3]{27 a^6 x^{12}-144 a^5 \cosh \left (3 c_1\right ) x^9-144 a^5 \sinh \left (3 c_1\right ) x^9+272 a^4 \cosh \left (6 c_1\right ) x^6+272 a^4 \sinh \left (6 c_1\right ) x^6-256 a^3 \cosh \left (9 c_1\right ) x^3-256 a^3 \sinh \left (9 c_1\right ) x^3+128 a^2 \cosh \left (12 c_1\right )+128 a^2 \sinh \left (12 c_1\right )+64 \sqrt {-a^9 \cosh \left (9 c_1\right ) x^{15}-a^9 \sinh \left (9 c_1\right ) x^{15}+7 a^8 \cosh \left (12 c_1\right ) x^{12}+7 a^8 \sinh \left (12 c_1\right ) x^{12}-19 a^7 \cosh \left (15 c_1\right ) x^9-19 a^7 \sinh \left (15 c_1\right ) x^9+25 a^6 \cosh \left (18 c_1\right ) x^6+25 a^6 \sinh \left (18 c_1\right ) x^6-16 a^5 \cosh \left (21 c_1\right ) x^3-16 a^5 \sinh \left (21 c_1\right ) x^3+4 a^4 \cosh \left (24 c_1\right )+4 a^4 \sinh \left (24 c_1\right )}}}+\frac {a^3 x^5}{\sqrt [3]{27 a^6 x^{12}-144 a^5 \cosh \left (3 c_1\right ) x^9-144 a^5 \sinh \left (3 c_1\right ) x^9+272 a^4 \cosh \left (6 c_1\right ) x^6+272 a^4 \sinh \left (6 c_1\right ) x^6-256 a^3 \cosh \left (9 c_1\right ) x^3-256 a^3 \sinh \left (9 c_1\right ) x^3+128 a^2 \cosh \left (12 c_1\right )+128 a^2 \sinh \left (12 c_1\right )+64 \sqrt {-a^9 \cosh \left (9 c_1\right ) x^{15}-a^9 \sinh \left (9 c_1\right ) x^{15}+7 a^8 \cosh \left (12 c_1\right ) x^{12}+7 a^8 \sinh \left (12 c_1\right ) x^{12}-19 a^7 \cosh \left (15 c_1\right ) x^9-19 a^7 \sinh \left (15 c_1\right ) x^9+25 a^6 \cosh \left (18 c_1\right ) x^6+25 a^6 \sinh \left (18 c_1\right ) x^6-16 a^5 \cosh \left (21 c_1\right ) x^3-16 a^5 \sinh \left (21 c_1\right ) x^3+4 a^4 \cosh \left (24 c_1\right )+4 a^4 \sinh \left (24 c_1\right )}}}+\frac {3}{16} a^2 \cosh \left (3 c_1\right ) x^4-\frac {3}{16} a^2 \sinh \left (3 c_1\right ) x^4-\frac {i \sqrt {3} a^2 \left (\cosh \left (3 c_1\right )+\sinh \left (3 c_1\right )\right ) x^2}{\sqrt [3]{27 a^6 x^{12}-144 a^5 \cosh \left (3 c_1\right ) x^9-144 a^5 \sinh \left (3 c_1\right ) x^9+272 a^4 \cosh \left (6 c_1\right ) x^6+272 a^4 \sinh \left (6 c_1\right ) x^6-256 a^3 \cosh \left (9 c_1\right ) x^3-256 a^3 \sinh \left (9 c_1\right ) x^3+128 a^2 \cosh \left (12 c_1\right )+128 a^2 \sinh \left (12 c_1\right )+64 \sqrt {-a^9 \cosh \left (9 c_1\right ) x^{15}-a^9 \sinh \left (9 c_1\right ) x^{15}+7 a^8 \cosh \left (12 c_1\right ) x^{12}+7 a^8 \sinh \left (12 c_1\right ) x^{12}-19 a^7 \cosh \left (15 c_1\right ) x^9-19 a^7 \sinh \left (15 c_1\right ) x^9+25 a^6 \cosh \left (18 c_1\right ) x^6+25 a^6 \sinh \left (18 c_1\right ) x^6-16 a^5 \cosh \left (21 c_1\right ) x^3-16 a^5 \sinh \left (21 c_1\right ) x^3+4 a^4 \cosh \left (24 c_1\right )+4 a^4 \sinh \left (24 c_1\right )}}}-\frac {a^2 \left (\cosh \left (3 c_1\right )+\sinh \left (3 c_1\right )\right ) x^2}{\sqrt [3]{27 a^6 x^{12}-144 a^5 \cosh \left (3 c_1\right ) x^9-144 a^5 \sinh \left (3 c_1\right ) x^9+272 a^4 \cosh \left (6 c_1\right ) x^6+272 a^4 \sinh \left (6 c_1\right ) x^6-256 a^3 \cosh \left (9 c_1\right ) x^3-256 a^3 \sinh \left (9 c_1\right ) x^3+128 a^2 \cosh \left (12 c_1\right )+128 a^2 \sinh \left (12 c_1\right )+64 \sqrt {-a^9 \cosh \left (9 c_1\right ) x^{15}-a^9 \sinh \left (9 c_1\right ) x^{15}+7 a^8 \cosh \left (12 c_1\right ) x^{12}+7 a^8 \sinh \left (12 c_1\right ) x^{12}-19 a^7 \cosh \left (15 c_1\right ) x^9-19 a^7 \sinh \left (15 c_1\right ) x^9+25 a^6 \cosh \left (18 c_1\right ) x^6+25 a^6 \sinh \left (18 c_1\right ) x^6-16 a^5 \cosh \left (21 c_1\right ) x^3-16 a^5 \sinh \left (21 c_1\right ) x^3+4 a^4 \cosh \left (24 c_1\right )+4 a^4 \sinh \left (24 c_1\right )}}}+a x+\frac {1}{32} i \sqrt {3} \left (\cosh \left (3 c_1\right )-\sinh \left (3 c_1\right )\right ) \sqrt [3]{27 a^6 x^{12}-144 a^5 \cosh \left (3 c_1\right ) x^9-144 a^5 \sinh \left (3 c_1\right ) x^9+272 a^4 \cosh \left (6 c_1\right ) x^6+272 a^4 \sinh \left (6 c_1\right ) x^6-256 a^3 \cosh \left (9 c_1\right ) x^3-256 a^3 \sinh \left (9 c_1\right ) x^3+128 a^2 \cosh \left (12 c_1\right )+128 a^2 \sinh \left (12 c_1\right )+64 \sqrt {-a^9 \cosh \left (9 c_1\right ) x^{15}-a^9 \sinh \left (9 c_1\right ) x^{15}+7 a^8 \cosh \left (12 c_1\right ) x^{12}+7 a^8 \sinh \left (12 c_1\right ) x^{12}-19 a^7 \cosh \left (15 c_1\right ) x^9-19 a^7 \sinh \left (15 c_1\right ) x^9+25 a^6 \cosh \left (18 c_1\right ) x^6+25 a^6 \sinh \left (18 c_1\right ) x^6-16 a^5 \cosh \left (21 c_1\right ) x^3-16 a^5 \sinh \left (21 c_1\right ) x^3+4 a^4 \cosh \left (24 c_1\right )+4 a^4 \sinh \left (24 c_1\right )}}-\frac {1}{32} \left (\cosh \left (3 c_1\right )-\sinh \left (3 c_1\right )\right ) \sqrt [3]{27 a^6 x^{12}-144 a^5 \cosh \left (3 c_1\right ) x^9-144 a^5 \sinh \left (3 c_1\right ) x^9+272 a^4 \cosh \left (6 c_1\right ) x^6+272 a^4 \sinh \left (6 c_1\right ) x^6-256 a^3 \cosh \left (9 c_1\right ) x^3-256 a^3 \sinh \left (9 c_1\right ) x^3+128 a^2 \cosh \left (12 c_1\right )+128 a^2 \sinh \left (12 c_1\right )+64 \sqrt {-a^9 \cosh \left (9 c_1\right ) x^{15}-a^9 \sinh \left (9 c_1\right ) x^{15}+7 a^8 \cosh \left (12 c_1\right ) x^{12}+7 a^8 \sinh \left (12 c_1\right ) x^{12}-19 a^7 \cosh \left (15 c_1\right ) x^9-19 a^7 \sinh \left (15 c_1\right ) x^9+25 a^6 \cosh \left (18 c_1\right ) x^6+25 a^6 \sinh \left (18 c_1\right ) x^6-16 a^5 \cosh \left (21 c_1\right ) x^3-16 a^5 \sinh \left (21 c_1\right ) x^3+4 a^4 \cosh \left (24 c_1\right )+4 a^4 \sinh \left (24 c_1\right )}}}\right \}\right \} \]
Maple: cpu = 0.546 (sec), leaf count = 897 \[ \left \{ y \left ( x \right ) ={\frac {x}{2} \left ( {\frac {1}{6\,{\it \_C1}}\sqrt [3]{-36\,a{{\it \_C1}}^{2}+8\,{x}^{3}+12\,\sqrt {a \left ( 9\,a{{\it \_C1}}^{2}-4\,{x}^{3} \right ) }{\it \_C1}}}+{\frac {2\,{x}^{ 2}}{3\,{\it \_C1}}{\frac {1}{\sqrt [3]{-36\,a{{\it \_C1}}^{2}+8\,{x}^{ 3}+12\,\sqrt {a \left ( 9\,a{{\it \_C1}}^{2}-4\,{x}^{3} \right ) }{\it \_C1}}}}}+{\frac {x}{3\,{\it \_C1}}} \right ) }+{\frac {a}{2} \left ( { \frac {1}{6\,{\it \_C1}}\sqrt [3]{-36\,a{{\it \_C1}}^{2}+8\,{x}^{3}+12 \,\sqrt {a \left ( 9\,a{{\it \_C1}}^{2}-4\,{x}^{3} \right ) }{\it \_C1}} }+{\frac {2\,{x}^{2}}{3\,{\it \_C1}}{\frac {1}{\sqrt [3]{-36\,a{{\it \_C1}}^{2}+8\,{x}^{3}+12\,\sqrt {a \left ( 9\,a{{\it \_C1}}^{2}-4\,{x}^ {3} \right ) }{\it \_C1}}}}}+{\frac {x}{3\,{\it \_C1}}} \right ) ^{-1}}, y \left ( x \right ) ={\frac {x}{2} \left ( -{\frac {1}{12\,{\it \_C1}} \sqrt [3]{-36\,a{{\it \_C1}}^{2}+8\,{x}^{3}+12\,\sqrt {a \left ( 9\,a{{ \it \_C1}}^{2}-4\,{x}^{3} \right ) }{\it \_C1}}}-{\frac {{x}^{2}}{3\,{ \it \_C1}}{\frac {1}{\sqrt [3]{-36\,a{{\it \_C1}}^{2}+8\,{x}^{3}+12\, \sqrt {a \left ( 9\,a{{\it \_C1}}^{2}-4\,{x}^{3} \right ) }{\it \_C1}}}} }+{\frac {x}{3\,{\it \_C1}}}-{\frac {i}{2}}\sqrt {3} \left ( {\frac {1 }{6\,{\it \_C1}}\sqrt [3]{-36\,a{{\it \_C1}}^{2}+8\,{x}^{3}+12\,\sqrt {a \left ( 9\,a{{\it \_C1}}^{2}-4\,{x}^{3} \right ) }{\it \_C1}}}-{ \frac {2\,{x}^{2}}{3\,{\it \_C1}}{\frac {1}{\sqrt [3]{-36\,a{{\it \_C1 }}^{2}+8\,{x}^{3}+12\,\sqrt {a \left ( 9\,a{{\it \_C1}}^{2}-4\,{x}^{3} \right ) }{\it \_C1}}}}} \right ) \right ) }+{\frac {a}{2} \left ( -{ \frac {1}{12\,{\it \_C1}}\sqrt [3]{-36\,a{{\it \_C1}}^{2}+8\,{x}^{3}+ 12\,\sqrt {a \left ( 9\,a{{\it \_C1}}^{2}-4\,{x}^{3} \right ) }{\it \_C1 }}}-{\frac {{x}^{2}}{3\,{\it \_C1}}{\frac {1}{\sqrt [3]{-36\,a{{\it \_C1}}^{2}+8\,{x}^{3}+12\,\sqrt {a \left ( 9\,a{{\it \_C1}}^{2}-4\,{x}^ {3} \right ) }{\it \_C1}}}}}+{\frac {x}{3\,{\it \_C1}}}-{\frac {i}{2}} \sqrt {3} \left ( {\frac {1}{6\,{\it \_C1}}\sqrt [3]{-36\,a{{\it \_C1}} ^{2}+8\,{x}^{3}+12\,\sqrt {a \left ( 9\,a{{\it \_C1}}^{2}-4\,{x}^{3} \right ) }{\it \_C1}}}-{\frac {2\,{x}^{2}}{3\,{\it \_C1}}{\frac {1}{ \sqrt [3]{-36\,a{{\it \_C1}}^{2}+8\,{x}^{3}+12\,\sqrt {a \left ( 9\,a{{ \it \_C1}}^{2}-4\,{x}^{3} \right ) }{\it \_C1}}}}} \right ) \right ) ^{- 1}},y \left ( x \right ) ={\frac {x}{2} \left ( -{\frac {1}{12\,{\it \_C1 }}\sqrt [3]{-36\,a{{\it \_C1}}^{2}+8\,{x}^{3}+12\,\sqrt {a \left ( 9\,a {{\it \_C1}}^{2}-4\,{x}^{3} \right ) }{\it \_C1}}}-{\frac {{x}^{2}}{3\, {\it \_C1}}{\frac {1}{\sqrt [3]{-36\,a{{\it \_C1}}^{2}+8\,{x}^{3}+12\, \sqrt {a \left ( 9\,a{{\it \_C1}}^{2}-4\,{x}^{3} \right ) }{\it \_C1}}}} }+{\frac {x}{3\,{\it \_C1}}}+{\frac {i}{2}}\sqrt {3} \left ( {\frac {1 }{6\,{\it \_C1}}\sqrt [3]{-36\,a{{\it \_C1}}^{2}+8\,{x}^{3}+12\,\sqrt {a \left ( 9\,a{{\it \_C1}}^{2}-4\,{x}^{3} \right ) }{\it \_C1}}}-{ \frac {2\,{x}^{2}}{3\,{\it \_C1}}{\frac {1}{\sqrt [3]{-36\,a{{\it \_C1 }}^{2}+8\,{x}^{3}+12\,\sqrt {a \left ( 9\,a{{\it \_C1}}^{2}-4\,{x}^{3} \right ) }{\it \_C1}}}}} \right ) \right ) }+{\frac {a}{2} \left ( -{ \frac {1}{12\,{\it \_C1}}\sqrt [3]{-36\,a{{\it \_C1}}^{2}+8\,{x}^{3}+ 12\,\sqrt {a \left ( 9\,a{{\it \_C1}}^{2}-4\,{x}^{3} \right ) }{\it \_C1 }}}-{\frac {{x}^{2}}{3\,{\it \_C1}}{\frac {1}{\sqrt [3]{-36\,a{{\it \_C1}}^{2}+8\,{x}^{3}+12\,\sqrt {a \left ( 9\,a{{\it \_C1}}^{2}-4\,{x}^ {3} \right ) }{\it \_C1}}}}}+{\frac {x}{3\,{\it \_C1}}}+{\frac {i}{2}} \sqrt {3} \left ( {\frac {1}{6\,{\it \_C1}}\sqrt [3]{-36\,a{{\it \_C1}} ^{2}+8\,{x}^{3}+12\,\sqrt {a \left ( 9\,a{{\it \_C1}}^{2}-4\,{x}^{3} \right ) }{\it \_C1}}}-{\frac {2\,{x}^{2}}{3\,{\it \_C1}}{\frac {1}{ \sqrt [3]{-36\,a{{\it \_C1}}^{2}+8\,{x}^{3}+12\,\sqrt {a \left ( 9\,a{{ \it \_C1}}^{2}-4\,{x}^{3} \right ) }{\it \_C1}}}}} \right ) \right ) ^{- 1}} \right \} \]