\[ a+x y'(x)^2-2 y(x) y'(x)=0 \] ✓ Mathematica : cpu = 1.69031 (sec), leaf count = 9391
\[\left \{\left \{y(x)\to -\frac {1}{4} \sqrt {\frac {9 a^4 \left (\cosh \left (3 c_1\right )-\sinh \left (3 c_1\right )\right ) x^8}{\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^4 \left (\left (a x^3-1\right ) \cosh \left (\frac {3 c_1}{2}\right )-\left (a x^3+1\right ) \sinh \left (\frac {3 c_1}{2}\right )\right ){}^3 \left (\left (a x^3-2\right ) \cosh \left (\frac {3 c_1}{2}\right )-\left (a x^3+2\right ) \sinh \left (\frac {3 c_1}{2}\right )\right ){}^2 \left (\cosh \left (\frac {33 c_1}{2}\right )+\sinh \left (\frac {33 c_1}{2}\right )\right )}}}-\frac {32 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^4 \left (\left (a x^3-1\right ) \cosh \left (\frac {3 c_1}{2}\right )-\left (a x^3+1\right ) \sinh \left (\frac {3 c_1}{2}\right )\right ){}^3 \left (\left (a x^3-2\right ) \cosh \left (\frac {3 c_1}{2}\right )-\left (a x^3+2\right ) \sinh \left (\frac {3 c_1}{2}\right )\right ){}^2 \left (\cosh \left (\frac {33 c_1}{2}\right )+\sinh \left (\frac {33 c_1}{2}\right )\right )}}}+3 a^2 \cosh \left (3 c_1\right ) x^4-3 a^2 \sinh \left (3 c_1\right ) x^4+\frac {32 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^4 \left (\left (a x^3-1\right ) \cosh \left (\frac {3 c_1}{2}\right )-\left (a x^3+1\right ) \sinh \left (\frac {3 c_1}{2}\right )\right ){}^3 \left (\left (a x^3-2\right ) \cosh \left (\frac {3 c_1}{2}\right )-\left (a x^3+2\right ) \sinh \left (\frac {3 c_1}{2}\right )\right ){}^2 \left (\cosh \left (\frac {33 c_1}{2}\right )+\sinh \left (\frac {33 c_1}{2}\right )\right )}}}+16 a x+\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^4 \left (\left (a x^3-1\right ) \cosh \left (\frac {3 c_1}{2}\right )-\left (a x^3+1\right ) \sinh \left (\frac {3 c_1}{2}\right )\right ){}^3 \left (\left (a x^3-2\right ) \cosh \left (\frac {3 c_1}{2}\right )-\left (a x^3+2\right ) \sinh \left (\frac {3 c_1}{2}\right )\right ){}^2 \left (\cosh \left (\frac {33 c_1}{2}\right )+\sinh \left (\frac {33 c_1}{2}\right )\right )}}}\right \},\left \{y(x)\to \frac {1}{4} \sqrt {\frac {9 a^4 \left (\cosh \left (3 c_1\right )-\sinh \left (3 c_1\right )\right ) x^8}{\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^4 \left (\left (a x^3-1\right ) \cosh \left (\frac {3 c_1}{2}\right )-\left (a x^3+1\right ) \sinh \left (\frac {3 c_1}{2}\right )\right ){}^3 \left (\left (a x^3-2\right ) \cosh \left (\frac {3 c_1}{2}\right )-\left (a x^3+2\right ) \sinh \left (\frac {3 c_1}{2}\right )\right ){}^2 \left (\cosh \left (\frac {33 c_1}{2}\right )+\sinh \left (\frac {33 c_1}{2}\right )\right )}}}-\frac {32 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^4 \left (\left (a x^3-1\right ) \cosh \left (\frac {3 c_1}{2}\right )-\left (a x^3+1\right ) \sinh \left (\frac {3 c_1}{2}\right )\right ){}^3 \left (\left (a x^3-2\right ) \cosh \left (\frac {3 c_1}{2}\right )-\left (a x^3+2\right ) \sinh \left (\frac {3 c_1}{2}\right )\right ){}^2 \left (\cosh \left (\frac {33 c_1}{2}\right )+\sinh \left (\frac {33 c_1}{2}\right )\right )}}}+3 a^2 \cosh \left (3 c_1\right ) x^4-3 a^2 \sinh \left (3 c_1\right ) x^4+\frac {32 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^4 \left (\left (a x^3-1\right ) \cosh \left (\frac {3 c_1}{2}\right )-\left (a x^3+1\right ) \sinh \left (\frac {3 c_1}{2}\right )\right ){}^3 \left (\left (a x^3-2\right ) \cosh \left (\frac {3 c_1}{2}\right )-\left (a x^3+2\right ) \sinh \left (\frac {3 c_1}{2}\right )\right ){}^2 \left (\cosh \left (\frac {33 c_1}{2}\right )+\sinh \left (\frac {33 c_1}{2}\right )\right )}}}+16 a x+\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^4 \left (\left (a x^3-1\right ) \cosh \left (\frac {3 c_1}{2}\right )-\left (a x^3+1\right ) \sinh \left (\frac {3 c_1}{2}\right )\right ){}^3 \left (\left (a x^3-2\right ) \cosh \left (\frac {3 c_1}{2}\right )-\left (a x^3+2\right ) \sinh \left (\frac {3 c_1}{2}\right )\right ){}^2 \left (\cosh \left (\frac {33 c_1}{2}\right )+\sinh \left (\frac {33 c_1}{2}\right )\right )}}}\right \},\left \{y(x)\to -\frac {\sqrt {\frac {9 i \sqrt {3} a^4 \cosh \left (3 c_1\right ) x^8-9 a^4 \cosh \left (3 c_1\right ) x^8-9 i \sqrt {3} a^4 \sinh \left (3 c_1\right ) x^8+9 a^4 \sinh \left (3 c_1\right ) x^8-32 i \sqrt {3} a^3 x^5+32 a^3 x^5+6 a^2 \cosh \left (3 c_1\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^4 \left (\left (a x^3-1\right ) \cosh \left (\frac {3 c_1}{2}\right )-\left (a x^3+1\right ) \sinh \left (\frac {3 c_1}{2}\right )\right ){}^3 \left (\left (a x^3-2\right ) \cosh \left (\frac {3 c_1}{2}\right )-\left (a x^3+2\right ) \sinh \left (\frac {3 c_1}{2}\right )\right ){}^2 \left (\cosh \left (\frac {33 c_1}{2}\right )+\sinh \left (\frac {33 c_1}{2}\right )\right )}} x^4-6 a^2 \sinh \left (3 c_1\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^4 \left (\left (a x^3-1\right ) \cosh \left (\frac {3 c_1}{2}\right )-\left (a x^3+1\right ) \sinh \left (\frac {3 c_1}{2}\right )\right ){}^3 \left (\left (a x^3-2\right ) \cosh \left (\frac {3 c_1}{2}\right )-\left (a x^3+2\right ) \sinh \left (\frac {3 c_1}{2}\right )\right ){}^2 \left (\cosh \left (\frac {33 c_1}{2}\right )+\sinh \left (\frac {33 c_1}{2}\right )\right )}} x^4+32 i \sqrt {3} a^2 \cosh \left (3 c_1\right ) x^2-32 a^2 \cosh \left (3 c_1\right ) x^2+32 i \sqrt {3} a^2 \sinh \left (3 c_1\right ) x^2-32 a^2 \sinh \left (3 c_1\right ) x^2+32 a \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^4 \left (\left (a x^3-1\right ) \cosh \left (\frac {3 c_1}{2}\right )-\left (a x^3+1\right ) \sinh \left (\frac {3 c_1}{2}\right )\right ){}^3 \left (\left (a x^3-2\right ) \cosh \left (\frac {3 c_1}{2}\right )-\left (a x^3+2\right ) \sinh \left (\frac {3 c_1}{2}\right )\right ){}^2 \left (\cosh \left (\frac {33 c_1}{2}\right )+\sinh \left (\frac {33 c_1}{2}\right )\right )}} x-i \sqrt {3} \cosh \left (3 c_1\right ) \left (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^4 \left (\left (a x^3-1\right ) \cosh \left (\frac {3 c_1}{2}\right )-\left (a x^3+1\right ) \sinh \left (\frac {3 c_1}{2}\right )\right ){}^3 \left (\left (a x^3-2\right ) \cosh \left (\frac {3 c_1}{2}\right )-\left (a x^3+2\right ) \sinh \left (\frac {3 c_1}{2}\right )\right ){}^2 \left (\cosh \left (\frac {33 c_1}{2}\right )+\sinh \left (\frac {33 c_1}{2}\right )\right )}\right ){}^{2/3}-\cosh \left (3 c_1\right ) \left (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^4 \left (\left (a x^3-1\right ) \cosh \left (\frac {3 c_1}{2}\right )-\left (a x^3+1\right ) \sinh \left (\frac {3 c_1}{2}\right )\right ){}^3 \left (\left (a x^3-2\right ) \cosh \left (\frac {3 c_1}{2}\right )-\left (a x^3+2\right ) \sinh \left (\frac {3 c_1}{2}\right )\right ){}^2 \left (\cosh \left (\frac {33 c_1}{2}\right )+\sinh \left (\frac {33 c_1}{2}\right )\right )}\right ){}^{2/3}+i \sqrt {3} \sinh \left (3 c_1\right ) \left (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^4 \left (\left (a x^3-1\right ) \cosh \left (\frac {3 c_1}{2}\right )-\left (a x^3+1\right ) \sinh \left (\frac {3 c_1}{2}\right )\right ){}^3 \left (\left (a x^3-2\right ) \cosh \left (\frac {3 c_1}{2}\right )-\left (a x^3+2\right ) \sinh \left (\frac {3 c_1}{2}\right )\right ){}^2 \left (\cosh \left (\frac {33 c_1}{2}\right )+\sinh \left (\frac {33 c_1}{2}\right )\right )}\right ){}^{2/3}+\sinh \left (3 c_1\right ) \left (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^4 \left (\left (a x^3-1\right ) \cosh \left (\frac {3 c_1}{2}\right )-\left (a x^3+1\right ) \sinh \left (\frac {3 c_1}{2}\right )\right ){}^3 \left (\left (a x^3-2\right ) \cosh \left (\frac {3 c_1}{2}\right )-\left (a x^3+2\right ) \sinh \left (\frac {3 c_1}{2}\right )\right ){}^2 \left (\cosh \left (\frac {33 c_1}{2}\right )+\sinh \left (\frac {33 c_1}{2}\right )\right )}\right ){}^{2/3}}{\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^4 \left (\left (a x^3-1\right ) \cosh \left (\frac {3 c_1}{2}\right )-\left (a x^3+1\right ) \sinh \left (\frac {3 c_1}{2}\right )\right ){}^3 \left (\left (a x^3-2\right ) \cosh \left (\frac {3 c_1}{2}\right )-\left (a x^3+2\right ) \sinh \left (\frac {3 c_1}{2}\right )\right ){}^2 \left (\cosh \left (\frac {33 c_1}{2}\right )+\sinh \left (\frac {33 c_1}{2}\right )\right )}}}}}{4 \sqrt {2}}\right \},\left \{y(x)\to \frac {\sqrt {\frac {9 i \sqrt {3} a^4 \cosh \left (3 c_1\right ) x^8-9 a^4 \cosh \left (3 c_1\right ) x^8-9 i \sqrt {3} a^4 \sinh \left (3 c_1\right ) x^8+9 a^4 \sinh \left (3 c_1\right ) x^8-32 i \sqrt {3} a^3 x^5+32 a^3 x^5+6 a^2 \cosh \left (3 c_1\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^4 \left (\left (a x^3-1\right ) \cosh \left (\frac {3 c_1}{2}\right )-\left (a x^3+1\right ) \sinh \left (\frac {3 c_1}{2}\right )\right ){}^3 \left (\left (a x^3-2\right ) \cosh \left (\frac {3 c_1}{2}\right )-\left (a x^3+2\right ) \sinh \left (\frac {3 c_1}{2}\right )\right ){}^2 \left (\cosh \left (\frac {33 c_1}{2}\right )+\sinh \left (\frac {33 c_1}{2}\right )\right )}} x^4-6 a^2 \sinh \left (3 c_1\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^4 \left (\left (a x^3-1\right ) \cosh \left (\frac {3 c_1}{2}\right )-\left (a x^3+1\right ) \sinh \left (\frac {3 c_1}{2}\right )\right ){}^3 \left (\left (a x^3-2\right ) \cosh \left (\frac {3 c_1}{2}\right )-\left (a x^3+2\right ) \sinh \left (\frac {3 c_1}{2}\right )\right ){}^2 \left (\cosh \left (\frac {33 c_1}{2}\right )+\sinh \left (\frac {33 c_1}{2}\right )\right )}} x^4+32 i \sqrt {3} a^2 \cosh \left (3 c_1\right ) x^2-32 a^2 \cosh \left (3 c_1\right ) x^2+32 i \sqrt {3} a^2 \sinh \left (3 c_1\right ) x^2-32 a^2 \sinh \left (3 c_1\right ) x^2+32 a \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^4 \left (\left (a x^3-1\right ) \cosh \left (\frac {3 c_1}{2}\right )-\left (a x^3+1\right ) \sinh \left (\frac {3 c_1}{2}\right )\right ){}^3 \left (\left (a x^3-2\right ) \cosh \left (\frac {3 c_1}{2}\right )-\left (a x^3+2\right ) \sinh \left (\frac {3 c_1}{2}\right )\right ){}^2 \left (\cosh \left (\frac {33 c_1}{2}\right )+\sinh \left (\frac {33 c_1}{2}\right )\right )}} x-i \sqrt {3} \cosh \left (3 c_1\right ) \left (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^4 \left (\left (a x^3-1\right ) \cosh \left (\frac {3 c_1}{2}\right )-\left (a x^3+1\right ) \sinh \left (\frac {3 c_1}{2}\right )\right ){}^3 \left (\left (a x^3-2\right ) \cosh \left (\frac {3 c_1}{2}\right )-\left (a x^3+2\right ) \sinh \left (\frac {3 c_1}{2}\right )\right ){}^2 \left (\cosh \left (\frac {33 c_1}{2}\right )+\sinh \left (\frac {33 c_1}{2}\right )\right )}\right ){}^{2/3}-\cosh \left (3 c_1\right ) \left (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^4 \left (\left (a x^3-1\right ) \cosh \left (\frac {3 c_1}{2}\right )-\left (a x^3+1\right ) \sinh \left (\frac {3 c_1}{2}\right )\right ){}^3 \left (\left (a x^3-2\right ) \cosh \left (\frac {3 c_1}{2}\right )-\left (a x^3+2\right ) \sinh \left (\frac {3 c_1}{2}\right )\right ){}^2 \left (\cosh \left (\frac {33 c_1}{2}\right )+\sinh \left (\frac {33 c_1}{2}\right )\right )}\right ){}^{2/3}+i \sqrt {3} \sinh \left (3 c_1\right ) \left (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^4 \left (\left (a x^3-1\right ) \cosh \left (\frac {3 c_1}{2}\right )-\left (a x^3+1\right ) \sinh \left (\frac {3 c_1}{2}\right )\right ){}^3 \left (\left (a x^3-2\right ) \cosh \left (\frac {3 c_1}{2}\right )-\left (a x^3+2\right ) \sinh \left (\frac {3 c_1}{2}\right )\right ){}^2 \left (\cosh \left (\frac {33 c_1}{2}\right )+\sinh \left (\frac {33 c_1}{2}\right )\right )}\right ){}^{2/3}+\sinh \left (3 c_1\right ) \left (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^4 \left (\left (a x^3-1\right ) \cosh \left (\frac {3 c_1}{2}\right )-\left (a x^3+1\right ) \sinh \left (\frac {3 c_1}{2}\right )\right ){}^3 \left (\left (a x^3-2\right ) \cosh \left (\frac {3 c_1}{2}\right )-\left (a x^3+2\right ) \sinh \left (\frac {3 c_1}{2}\right )\right ){}^2 \left (\cosh \left (\frac {33 c_1}{2}\right )+\sinh \left (\frac {33 c_1}{2}\right )\right )}\right ){}^{2/3}}{\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^4 \left (\left (a x^3-1\right ) \cosh \left (\frac {3 c_1}{2}\right )-\left (a x^3+1\right ) \sinh \left (\frac {3 c_1}{2}\right )\right ){}^3 \left (\left (a x^3-2\right ) \cosh \left (\frac {3 c_1}{2}\right )-\left (a x^3+2\right ) \sinh \left (\frac {3 c_1}{2}\right )\right ){}^2 \left (\cosh \left (\frac {33 c_1}{2}\right )+\sinh \left (\frac {33 c_1}{2}\right )\right )}}}}}{4 \sqrt {2}}\right \},\left \{y(x)\to -\frac {\sqrt {\frac {-9 i \sqrt {3} a^4 \cosh \left (3 c_1\right ) x^8-9 a^4 \cosh \left (3 c_1\right ) x^8+9 i \sqrt {3} a^4 \sinh \left (3 c_1\right ) x^8+9 a^4 \sinh \left (3 c_1\right ) x^8+32 i \sqrt {3} a^3 x^5+32 a^3 x^5+6 a^2 \cosh \left (3 c_1\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^4 \left (\left (a x^3-1\right ) \cosh \left (\frac {3 c_1}{2}\right )-\left (a x^3+1\right ) \sinh \left (\frac {3 c_1}{2}\right )\right ){}^3 \left (\left (a x^3-2\right ) \cosh \left (\frac {3 c_1}{2}\right )-\left (a x^3+2\right ) \sinh \left (\frac {3 c_1}{2}\right )\right ){}^2 \left (\cosh \left (\frac {33 c_1}{2}\right )+\sinh \left (\frac {33 c_1}{2}\right )\right )}} x^4-6 a^2 \sinh \left (3 c_1\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^4 \left (\left (a x^3-1\right ) \cosh \left (\frac {3 c_1}{2}\right )-\left (a x^3+1\right ) \sinh \left (\frac {3 c_1}{2}\right )\right ){}^3 \left (\left (a x^3-2\right ) \cosh \left (\frac {3 c_1}{2}\right )-\left (a x^3+2\right ) \sinh \left (\frac {3 c_1}{2}\right )\right ){}^2 \left (\cosh \left (\frac {33 c_1}{2}\right )+\sinh \left (\frac {33 c_1}{2}\right )\right )}} x^4-32 i \sqrt {3} a^2 \cosh \left (3 c_1\right ) x^2-32 a^2 \cosh \left (3 c_1\right ) x^2-32 i \sqrt {3} a^2 \sinh \left (3 c_1\right ) x^2-32 a^2 \sinh \left (3 c_1\right ) x^2+32 a \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^4 \left (\left (a x^3-1\right ) \cosh \left (\frac {3 c_1}{2}\right )-\left (a x^3+1\right ) \sinh \left (\frac {3 c_1}{2}\right )\right ){}^3 \left (\left (a x^3-2\right ) \cosh \left (\frac {3 c_1}{2}\right )-\left (a x^3+2\right ) \sinh \left (\frac {3 c_1}{2}\right )\right ){}^2 \left (\cosh \left (\frac {33 c_1}{2}\right )+\sinh \left (\frac {33 c_1}{2}\right )\right )}} x+i \sqrt {3} \cosh \left (3 c_1\right ) \left (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^4 \left (\left (a x^3-1\right ) \cosh \left (\frac {3 c_1}{2}\right )-\left (a x^3+1\right ) \sinh \left (\frac {3 c_1}{2}\right )\right ){}^3 \left (\left (a x^3-2\right ) \cosh \left (\frac {3 c_1}{2}\right )-\left (a x^3+2\right ) \sinh \left (\frac {3 c_1}{2}\right )\right ){}^2 \left (\cosh \left (\frac {33 c_1}{2}\right )+\sinh \left (\frac {33 c_1}{2}\right )\right )}\right ){}^{2/3}-\cosh \left (3 c_1\right ) \left (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^4 \left (\left (a x^3-1\right ) \cosh \left (\frac {3 c_1}{2}\right )-\left (a x^3+1\right ) \sinh \left (\frac {3 c_1}{2}\right )\right ){}^3 \left (\left (a x^3-2\right ) \cosh \left (\frac {3 c_1}{2}\right )-\left (a x^3+2\right ) \sinh \left (\frac {3 c_1}{2}\right )\right ){}^2 \left (\cosh \left (\frac {33 c_1}{2}\right )+\sinh \left (\frac {33 c_1}{2}\right )\right )}\right ){}^{2/3}-i \sqrt {3} \sinh \left (3 c_1\right ) \left (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^4 \left (\left (a x^3-1\right ) \cosh \left (\frac {3 c_1}{2}\right )-\left (a x^3+1\right ) \sinh \left (\frac {3 c_1}{2}\right )\right ){}^3 \left (\left (a x^3-2\right ) \cosh \left (\frac {3 c_1}{2}\right )-\left (a x^3+2\right ) \sinh \left (\frac {3 c_1}{2}\right )\right ){}^2 \left (\cosh \left (\frac {33 c_1}{2}\right )+\sinh \left (\frac {33 c_1}{2}\right )\right )}\right ){}^{2/3}+\sinh \left (3 c_1\right ) \left (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^4 \left (\left (a x^3-1\right ) \cosh \left (\frac {3 c_1}{2}\right )-\left (a x^3+1\right ) \sinh \left (\frac {3 c_1}{2}\right )\right ){}^3 \left (\left (a x^3-2\right ) \cosh \left (\frac {3 c_1}{2}\right )-\left (a x^3+2\right ) \sinh \left (\frac {3 c_1}{2}\right )\right ){}^2 \left (\cosh \left (\frac {33 c_1}{2}\right )+\sinh \left (\frac {33 c_1}{2}\right )\right )}\right ){}^{2/3}}{\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^4 \left (\left (a x^3-1\right ) \cosh \left (\frac {3 c_1}{2}\right )-\left (a x^3+1\right ) \sinh \left (\frac {3 c_1}{2}\right )\right ){}^3 \left (\left (a x^3-2\right ) \cosh \left (\frac {3 c_1}{2}\right )-\left (a x^3+2\right ) \sinh \left (\frac {3 c_1}{2}\right )\right ){}^2 \left (\cosh \left (\frac {33 c_1}{2}\right )+\sinh \left (\frac {33 c_1}{2}\right )\right )}}}}}{4 \sqrt {2}}\right \},\left \{y(x)\to \frac {\sqrt {\frac {-9 i \sqrt {3} a^4 \cosh \left (3 c_1\right ) x^8-9 a^4 \cosh \left (3 c_1\right ) x^8+9 i \sqrt {3} a^4 \sinh \left (3 c_1\right ) x^8+9 a^4 \sinh \left (3 c_1\right ) x^8+32 i \sqrt {3} a^3 x^5+32 a^3 x^5+6 a^2 \cosh \left (3 c_1\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^4 \left (\left (a x^3-1\right ) \cosh \left (\frac {3 c_1}{2}\right )-\left (a x^3+1\right ) \sinh \left (\frac {3 c_1}{2}\right )\right ){}^3 \left (\left (a x^3-2\right ) \cosh \left (\frac {3 c_1}{2}\right )-\left (a x^3+2\right ) \sinh \left (\frac {3 c_1}{2}\right )\right ){}^2 \left (\cosh \left (\frac {33 c_1}{2}\right )+\sinh \left (\frac {33 c_1}{2}\right )\right )}} x^4-6 a^2 \sinh \left (3 c_1\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^4 \left (\left (a x^3-1\right ) \cosh \left (\frac {3 c_1}{2}\right )-\left (a x^3+1\right ) \sinh \left (\frac {3 c_1}{2}\right )\right ){}^3 \left (\left (a x^3-2\right ) \cosh \left (\frac {3 c_1}{2}\right )-\left (a x^3+2\right ) \sinh \left (\frac {3 c_1}{2}\right )\right ){}^2 \left (\cosh \left (\frac {33 c_1}{2}\right )+\sinh \left (\frac {33 c_1}{2}\right )\right )}} x^4-32 i \sqrt {3} a^2 \cosh \left (3 c_1\right ) x^2-32 a^2 \cosh \left (3 c_1\right ) x^2-32 i \sqrt {3} a^2 \sinh \left (3 c_1\right ) x^2-32 a^2 \sinh \left (3 c_1\right ) x^2+32 a \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^4 \left (\left (a x^3-1\right ) \cosh \left (\frac {3 c_1}{2}\right )-\left (a x^3+1\right ) \sinh \left (\frac {3 c_1}{2}\right )\right ){}^3 \left (\left (a x^3-2\right ) \cosh \left (\frac {3 c_1}{2}\right )-\left (a x^3+2\right ) \sinh \left (\frac {3 c_1}{2}\right )\right ){}^2 \left (\cosh \left (\frac {33 c_1}{2}\right )+\sinh \left (\frac {33 c_1}{2}\right )\right )}} x+i \sqrt {3} \cosh \left (3 c_1\right ) \left (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^4 \left (\left (a x^3-1\right ) \cosh \left (\frac {3 c_1}{2}\right )-\left (a x^3+1\right ) \sinh \left (\frac {3 c_1}{2}\right )\right ){}^3 \left (\left (a x^3-2\right ) \cosh \left (\frac {3 c_1}{2}\right )-\left (a x^3+2\right ) \sinh \left (\frac {3 c_1}{2}\right )\right ){}^2 \left (\cosh \left (\frac {33 c_1}{2}\right )+\sinh \left (\frac {33 c_1}{2}\right )\right )}\right ){}^{2/3}-\cosh \left (3 c_1\right ) \left (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^4 \left (\left (a x^3-1\right ) \cosh \left (\frac {3 c_1}{2}\right )-\left (a x^3+1\right ) \sinh \left (\frac {3 c_1}{2}\right )\right ){}^3 \left (\left (a x^3-2\right ) \cosh \left (\frac {3 c_1}{2}\right )-\left (a x^3+2\right ) \sinh \left (\frac {3 c_1}{2}\right )\right ){}^2 \left (\cosh \left (\frac {33 c_1}{2}\right )+\sinh \left (\frac {33 c_1}{2}\right )\right )}\right ){}^{2/3}-i \sqrt {3} \sinh \left (3 c_1\right ) \left (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^4 \left (\left (a x^3-1\right ) \cosh \left (\frac {3 c_1}{2}\right )-\left (a x^3+1\right ) \sinh \left (\frac {3 c_1}{2}\right )\right ){}^3 \left (\left (a x^3-2\right ) \cosh \left (\frac {3 c_1}{2}\right )-\left (a x^3+2\right ) \sinh \left (\frac {3 c_1}{2}\right )\right ){}^2 \left (\cosh \left (\frac {33 c_1}{2}\right )+\sinh \left (\frac {33 c_1}{2}\right )\right )}\right ){}^{2/3}+\sinh \left (3 c_1\right ) \left (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^4 \left (\left (a x^3-1\right ) \cosh \left (\frac {3 c_1}{2}\right )-\left (a x^3+1\right ) \sinh \left (\frac {3 c_1}{2}\right )\right ){}^3 \left (\left (a x^3-2\right ) \cosh \left (\frac {3 c_1}{2}\right )-\left (a x^3+2\right ) \sinh \left (\frac {3 c_1}{2}\right )\right ){}^2 \left (\cosh \left (\frac {33 c_1}{2}\right )+\sinh \left (\frac {33 c_1}{2}\right )\right )}\right ){}^{2/3}}{\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^4 \left (\left (a x^3-1\right ) \cosh \left (\frac {3 c_1}{2}\right )-\left (a x^3+1\right ) \sinh \left (\frac {3 c_1}{2}\right )\right ){}^3 \left (\left (a x^3-2\right ) \cosh \left (\frac {3 c_1}{2}\right )-\left (a x^3+2\right ) \sinh \left (\frac {3 c_1}{2}\right )\right ){}^2 \left (\cosh \left (\frac {33 c_1}{2}\right )+\sinh \left (\frac {33 c_1}{2}\right )\right )}}}}}{4 \sqrt {2}}\right \}\right \}\]
✓ Maple : cpu = 0.038 (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 ( 1+i\sqrt {3} \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 ( 1+i\sqrt {3} \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 ( {{x}^{2} \left ( i\sqrt {3}-1 \right ) {\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 {{x}^{2} \left ( i\sqrt {3}-1 \right ) }{\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 \} \]