\[ a+x y'(x)^2-2 y(x) y'(x)=0 \] ✓ Mathematica : cpu = 1.98725 (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 = 0.808 (sec), leaf count = 689
\[ \left \{ y \left ( x \right ) ={\frac {x}{12\,{\it \_C1}} \left ( 4\,{\frac {{x}^{2}}{\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}}}}+2\,x+\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 ) }+3\,{{\it \_C1}\,a \left ( 4\,{\frac {{x}^{2}}{\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}}}}+2\,x+\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 ) ^{-1}},y \left ( x \right ) ={\frac {x}{6\,{\it \_C1}} \left ( { \left ( i\sqrt {3}-1 \right ) {x}^{2}{\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 {i}{4}}\sqrt {3}\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}}+x-{\frac {1}{4}\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 ) }+6\,{{\it \_C1}\,a \left ( 4\,{\frac { \left ( i\sqrt {3}-1 \right ) {x}^{2}}{\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}}}}-i\sqrt {3}\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}}+4\,x-\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 ) ^{-1}},y \left ( x \right ) =-{\frac {x}{6\,{\it \_C1}} \left ( { \left ( i\sqrt {3}+1 \right ) {x}^{2}{\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 {i}{4}}\sqrt {3}\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}}-x+{\frac {1}{4}\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 ) }-6\,{{\it \_C1}\,a \left ( 4\,{\frac { \left ( i\sqrt {3}+1 \right ) {x}^{2}}{\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}}}}-i\sqrt {3}\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}}-4\,x+\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 ) ^{-1}} \right \} \]