#### 2.443   ODE No. 443

$x \left (x y'(x)-y(x)\right )^2-y'(x)=0$ Mathematica : cpu = 2.74856 (sec), leaf count = 10121

$\left \{\left \{y(x)\to -\frac {1}{2} \sqrt {-\frac {4}{9} \cosh (6 c_1) x^2+\frac {4}{9} \sinh (6 c_1) x^2+\frac {\sqrt [3]{2} \sqrt [3]{-32 \cosh (18 c_1) x^{12}+32 \sinh (18 c_1) x^{12}+40 \cosh (12 c_1) x^6-40 \sinh (12 c_1) x^6+\cosh (6 c_1)-\sinh (6 c_1)+(\cosh (36 c_1)-\sinh (36 c_1)) \sqrt {-4096 \cosh (42 c_1) x^{18}-4096 \sinh (42 c_1) x^{18}+768 \cosh (48 c_1) x^{12}+768 \sinh (48 c_1) x^{12}-48 \cosh (54 c_1) x^6-48 \sinh (54 c_1) x^6+\cosh (60 c_1)+\sinh (60 c_1)}}}{9 x^2}+\frac {4\ 2^{2/3} \left (2 \cosh (12 c_1) x^8+2 \sinh (12 c_1) x^8+\cosh (18 c_1) x^2+\sinh (18 c_1) x^2\right ) (\cosh (24 c_1)-\sinh (24 c_1))}{9 \sqrt [3]{-32 \cosh (18 c_1) x^{12}+32 \sinh (18 c_1) x^{12}+40 \cosh (12 c_1) x^6-40 \sinh (12 c_1) x^6+\cosh (6 c_1)-\sinh (6 c_1)+(\cosh (36 c_1)-\sinh (36 c_1)) \sqrt {-4096 \cosh (42 c_1) x^{18}-4096 \sinh (42 c_1) x^{18}+768 \cosh (48 c_1) x^{12}+768 \sinh (48 c_1) x^{12}-48 \cosh (54 c_1) x^6-48 \sinh (54 c_1) x^6+\cosh (60 c_1)+\sinh (60 c_1)}} x^2}+\frac {1}{81 x^4}}-\frac {1}{2} \sqrt {-\frac {8}{9} \cosh (6 c_1) x^2+\frac {8}{9} \sinh (6 c_1) x^2-\frac {-\frac {128}{27} \cosh (6 c_1)+\frac {128}{27} \sinh (6 c_1)-\frac {8}{729 x^6}}{4 \sqrt {-\frac {4}{9} \cosh (6 c_1) x^2+\frac {4}{9} \sinh (6 c_1) x^2+\frac {\sqrt [3]{2} \sqrt [3]{-32 \cosh (18 c_1) x^{12}+32 \sinh (18 c_1) x^{12}+40 \cosh (12 c_1) x^6-40 \sinh (12 c_1) x^6+\cosh (6 c_1)-\sinh (6 c_1)+(\cosh (36 c_1)-\sinh (36 c_1)) \sqrt {-4096 \cosh (42 c_1) x^{18}-4096 \sinh (42 c_1) x^{18}+768 \cosh (48 c_1) x^{12}+768 \sinh (48 c_1) x^{12}-48 \cosh (54 c_1) x^6-48 \sinh (54 c_1) x^6+\cosh (60 c_1)+\sinh (60 c_1)}}}{9 x^2}+\frac {4\ 2^{2/3} \left (2 \cosh (12 c_1) x^8+2 \sinh (12 c_1) x^8+\cosh (18 c_1) x^2+\sinh (18 c_1) x^2\right ) (\cosh (24 c_1)-\sinh (24 c_1))}{9 \sqrt [3]{-32 \cosh (18 c_1) x^{12}+32 \sinh (18 c_1) x^{12}+40 \cosh (12 c_1) x^6-40 \sinh (12 c_1) x^6+\cosh (6 c_1)-\sinh (6 c_1)+(\cosh (36 c_1)-\sinh (36 c_1)) \sqrt {-4096 \cosh (42 c_1) x^{18}-4096 \sinh (42 c_1) x^{18}+768 \cosh (48 c_1) x^{12}+768 \sinh (48 c_1) x^{12}-48 \cosh (54 c_1) x^6-48 \sinh (54 c_1) x^6+\cosh (60 c_1)+\sinh (60 c_1)}} x^2}+\frac {1}{81 x^4}}}-\frac {\sqrt [3]{2} \sqrt [3]{-32 \cosh (18 c_1) x^{12}+32 \sinh (18 c_1) x^{12}+40 \cosh (12 c_1) x^6-40 \sinh (12 c_1) x^6+\cosh (6 c_1)-\sinh (6 c_1)+(\cosh (36 c_1)-\sinh (36 c_1)) \sqrt {-4096 \cosh (42 c_1) x^{18}-4096 \sinh (42 c_1) x^{18}+768 \cosh (48 c_1) x^{12}+768 \sinh (48 c_1) x^{12}-48 \cosh (54 c_1) x^6-48 \sinh (54 c_1) x^6+\cosh (60 c_1)+\sinh (60 c_1)}}}{9 x^2}-\frac {4\ 2^{2/3} \left (2 \cosh (12 c_1) x^8+2 \sinh (12 c_1) x^8+\cosh (18 c_1) x^2+\sinh (18 c_1) x^2\right ) (\cosh (24 c_1)-\sinh (24 c_1))}{9 \sqrt [3]{-32 \cosh (18 c_1) x^{12}+32 \sinh (18 c_1) x^{12}+40 \cosh (12 c_1) x^6-40 \sinh (12 c_1) x^6+\cosh (6 c_1)-\sinh (6 c_1)+(\cosh (36 c_1)-\sinh (36 c_1)) \sqrt {-4096 \cosh (42 c_1) x^{18}-4096 \sinh (42 c_1) x^{18}+768 \cosh (48 c_1) x^{12}+768 \sinh (48 c_1) x^{12}-48 \cosh (54 c_1) x^6-48 \sinh (54 c_1) x^6+\cosh (60 c_1)+\sinh (60 c_1)}} x^2}+\frac {2}{81 x^4}}-\frac {1}{18 x^2}\right \},\left \{y(x)\to -\frac {1}{2} \sqrt {-\frac {4}{9} \cosh (6 c_1) x^2+\frac {4}{9} \sinh (6 c_1) x^2+\frac {\sqrt [3]{2} \sqrt [3]{-32 \cosh (18 c_1) x^{12}+32 \sinh (18 c_1) x^{12}+40 \cosh (12 c_1) x^6-40 \sinh (12 c_1) x^6+\cosh (6 c_1)-\sinh (6 c_1)+(\cosh (36 c_1)-\sinh (36 c_1)) \sqrt {-4096 \cosh (42 c_1) x^{18}-4096 \sinh (42 c_1) x^{18}+768 \cosh (48 c_1) x^{12}+768 \sinh (48 c_1) x^{12}-48 \cosh (54 c_1) x^6-48 \sinh (54 c_1) x^6+\cosh (60 c_1)+\sinh (60 c_1)}}}{9 x^2}+\frac {4\ 2^{2/3} \left (2 \cosh (12 c_1) x^8+2 \sinh (12 c_1) x^8+\cosh (18 c_1) x^2+\sinh (18 c_1) x^2\right ) (\cosh (24 c_1)-\sinh (24 c_1))}{9 \sqrt [3]{-32 \cosh (18 c_1) x^{12}+32 \sinh (18 c_1) x^{12}+40 \cosh (12 c_1) x^6-40 \sinh (12 c_1) x^6+\cosh (6 c_1)-\sinh (6 c_1)+(\cosh (36 c_1)-\sinh (36 c_1)) \sqrt {-4096 \cosh (42 c_1) x^{18}-4096 \sinh (42 c_1) x^{18}+768 \cosh (48 c_1) x^{12}+768 \sinh (48 c_1) x^{12}-48 \cosh (54 c_1) x^6-48 \sinh (54 c_1) x^6+\cosh (60 c_1)+\sinh (60 c_1)}} x^2}+\frac {1}{81 x^4}}+\frac {1}{2} \sqrt {-\frac {8}{9} \cosh (6 c_1) x^2+\frac {8}{9} \sinh (6 c_1) x^2-\frac {-\frac {128}{27} \cosh (6 c_1)+\frac {128}{27} \sinh (6 c_1)-\frac {8}{729 x^6}}{4 \sqrt {-\frac {4}{9} \cosh (6 c_1) x^2+\frac {4}{9} \sinh (6 c_1) x^2+\frac {\sqrt [3]{2} \sqrt [3]{-32 \cosh (18 c_1) x^{12}+32 \sinh (18 c_1) x^{12}+40 \cosh (12 c_1) x^6-40 \sinh (12 c_1) x^6+\cosh (6 c_1)-\sinh (6 c_1)+(\cosh (36 c_1)-\sinh (36 c_1)) \sqrt {-4096 \cosh (42 c_1) x^{18}-4096 \sinh (42 c_1) x^{18}+768 \cosh (48 c_1) x^{12}+768 \sinh (48 c_1) x^{12}-48 \cosh (54 c_1) x^6-48 \sinh (54 c_1) x^6+\cosh (60 c_1)+\sinh (60 c_1)}}}{9 x^2}+\frac {4\ 2^{2/3} \left (2 \cosh (12 c_1) x^8+2 \sinh (12 c_1) x^8+\cosh (18 c_1) x^2+\sinh (18 c_1) x^2\right ) (\cosh (24 c_1)-\sinh (24 c_1))}{9 \sqrt [3]{-32 \cosh (18 c_1) x^{12}+32 \sinh (18 c_1) x^{12}+40 \cosh (12 c_1) x^6-40 \sinh (12 c_1) x^6+\cosh (6 c_1)-\sinh (6 c_1)+(\cosh (36 c_1)-\sinh (36 c_1)) \sqrt {-4096 \cosh (42 c_1) x^{18}-4096 \sinh (42 c_1) x^{18}+768 \cosh (48 c_1) x^{12}+768 \sinh (48 c_1) x^{12}-48 \cosh (54 c_1) x^6-48 \sinh (54 c_1) x^6+\cosh (60 c_1)+\sinh (60 c_1)}} x^2}+\frac {1}{81 x^4}}}-\frac {\sqrt [3]{2} \sqrt [3]{-32 \cosh (18 c_1) x^{12}+32 \sinh (18 c_1) x^{12}+40 \cosh (12 c_1) x^6-40 \sinh (12 c_1) x^6+\cosh (6 c_1)-\sinh (6 c_1)+(\cosh (36 c_1)-\sinh (36 c_1)) \sqrt {-4096 \cosh (42 c_1) x^{18}-4096 \sinh (42 c_1) x^{18}+768 \cosh (48 c_1) x^{12}+768 \sinh (48 c_1) x^{12}-48 \cosh (54 c_1) x^6-48 \sinh (54 c_1) x^6+\cosh (60 c_1)+\sinh (60 c_1)}}}{9 x^2}-\frac {4\ 2^{2/3} \left (2 \cosh (12 c_1) x^8+2 \sinh (12 c_1) x^8+\cosh (18 c_1) x^2+\sinh (18 c_1) x^2\right ) (\cosh (24 c_1)-\sinh (24 c_1))}{9 \sqrt [3]{-32 \cosh (18 c_1) x^{12}+32 \sinh (18 c_1) x^{12}+40 \cosh (12 c_1) x^6-40 \sinh (12 c_1) x^6+\cosh (6 c_1)-\sinh (6 c_1)+(\cosh (36 c_1)-\sinh (36 c_1)) \sqrt {-4096 \cosh (42 c_1) x^{18}-4096 \sinh (42 c_1) x^{18}+768 \cosh (48 c_1) x^{12}+768 \sinh (48 c_1) x^{12}-48 \cosh (54 c_1) x^6-48 \sinh (54 c_1) x^6+\cosh (60 c_1)+\sinh (60 c_1)}} x^2}+\frac {2}{81 x^4}}-\frac {1}{18 x^2}\right \},\left \{y(x)\to \frac {1}{2} \sqrt {-\frac {4}{9} \cosh (6 c_1) x^2+\frac {4}{9} \sinh (6 c_1) x^2+\frac {\sqrt [3]{2} \sqrt [3]{-32 \cosh (18 c_1) x^{12}+32 \sinh (18 c_1) x^{12}+40 \cosh (12 c_1) x^6-40 \sinh (12 c_1) x^6+\cosh (6 c_1)-\sinh (6 c_1)+(\cosh (36 c_1)-\sinh (36 c_1)) \sqrt {-4096 \cosh (42 c_1) x^{18}-4096 \sinh (42 c_1) x^{18}+768 \cosh (48 c_1) x^{12}+768 \sinh (48 c_1) x^{12}-48 \cosh (54 c_1) x^6-48 \sinh (54 c_1) x^6+\cosh (60 c_1)+\sinh (60 c_1)}}}{9 x^2}+\frac {4\ 2^{2/3} \left (2 \cosh (12 c_1) x^8+2 \sinh (12 c_1) x^8+\cosh (18 c_1) x^2+\sinh (18 c_1) x^2\right ) (\cosh (24 c_1)-\sinh (24 c_1))}{9 \sqrt [3]{-32 \cosh (18 c_1) x^{12}+32 \sinh (18 c_1) x^{12}+40 \cosh (12 c_1) x^6-40 \sinh (12 c_1) x^6+\cosh (6 c_1)-\sinh (6 c_1)+(\cosh (36 c_1)-\sinh (36 c_1)) \sqrt {-4096 \cosh (42 c_1) x^{18}-4096 \sinh (42 c_1) x^{18}+768 \cosh (48 c_1) x^{12}+768 \sinh (48 c_1) x^{12}-48 \cosh (54 c_1) x^6-48 \sinh (54 c_1) x^6+\cosh (60 c_1)+\sinh (60 c_1)}} x^2}+\frac {1}{81 x^4}}-\frac {1}{2} \sqrt {-\frac {8}{9} \cosh (6 c_1) x^2+\frac {8}{9} \sinh (6 c_1) x^2+\frac {-\frac {128}{27} \cosh (6 c_1)+\frac {128}{27} \sinh (6 c_1)-\frac {8}{729 x^6}}{4 \sqrt {-\frac {4}{9} \cosh (6 c_1) x^2+\frac {4}{9} \sinh (6 c_1) x^2+\frac {\sqrt [3]{2} \sqrt [3]{-32 \cosh (18 c_1) x^{12}+32 \sinh (18 c_1) x^{12}+40 \cosh (12 c_1) x^6-40 \sinh (12 c_1) x^6+\cosh (6 c_1)-\sinh (6 c_1)+(\cosh (36 c_1)-\sinh (36 c_1)) \sqrt {-4096 \cosh (42 c_1) x^{18}-4096 \sinh (42 c_1) x^{18}+768 \cosh (48 c_1) x^{12}+768 \sinh (48 c_1) x^{12}-48 \cosh (54 c_1) x^6-48 \sinh (54 c_1) x^6+\cosh (60 c_1)+\sinh (60 c_1)}}}{9 x^2}+\frac {4\ 2^{2/3} \left (2 \cosh (12 c_1) x^8+2 \sinh (12 c_1) x^8+\cosh (18 c_1) x^2+\sinh (18 c_1) x^2\right ) (\cosh (24 c_1)-\sinh (24 c_1))}{9 \sqrt [3]{-32 \cosh (18 c_1) x^{12}+32 \sinh (18 c_1) x^{12}+40 \cosh (12 c_1) x^6-40 \sinh (12 c_1) x^6+\cosh (6 c_1)-\sinh (6 c_1)+(\cosh (36 c_1)-\sinh (36 c_1)) \sqrt {-4096 \cosh (42 c_1) x^{18}-4096 \sinh (42 c_1) x^{18}+768 \cosh (48 c_1) x^{12}+768 \sinh (48 c_1) x^{12}-48 \cosh (54 c_1) x^6-48 \sinh (54 c_1) x^6+\cosh (60 c_1)+\sinh (60 c_1)}} x^2}+\frac {1}{81 x^4}}}-\frac {\sqrt [3]{2} \sqrt [3]{-32 \cosh (18 c_1) x^{12}+32 \sinh (18 c_1) x^{12}+40 \cosh (12 c_1) x^6-40 \sinh (12 c_1) x^6+\cosh (6 c_1)-\sinh (6 c_1)+(\cosh (36 c_1)-\sinh (36 c_1)) \sqrt {-4096 \cosh (42 c_1) x^{18}-4096 \sinh (42 c_1) x^{18}+768 \cosh (48 c_1) x^{12}+768 \sinh (48 c_1) x^{12}-48 \cosh (54 c_1) x^6-48 \sinh (54 c_1) x^6+\cosh (60 c_1)+\sinh (60 c_1)}}}{9 x^2}-\frac {4\ 2^{2/3} \left (2 \cosh (12 c_1) x^8+2 \sinh (12 c_1) x^8+\cosh (18 c_1) x^2+\sinh (18 c_1) x^2\right ) (\cosh (24 c_1)-\sinh (24 c_1))}{9 \sqrt [3]{-32 \cosh (18 c_1) x^{12}+32 \sinh (18 c_1) x^{12}+40 \cosh (12 c_1) x^6-40 \sinh (12 c_1) x^6+\cosh (6 c_1)-\sinh (6 c_1)+(\cosh (36 c_1)-\sinh (36 c_1)) \sqrt {-4096 \cosh (42 c_1) x^{18}-4096 \sinh (42 c_1) x^{18}+768 \cosh (48 c_1) x^{12}+768 \sinh (48 c_1) x^{12}-48 \cosh (54 c_1) x^6-48 \sinh (54 c_1) x^6+\cosh (60 c_1)+\sinh (60 c_1)}} x^2}+\frac {2}{81 x^4}}-\frac {1}{18 x^2}\right \},\left \{y(x)\to \frac {1}{2} \sqrt {-\frac {4}{9} \cosh (6 c_1) x^2+\frac {4}{9} \sinh (6 c_1) x^2+\frac {\sqrt [3]{2} \sqrt [3]{-32 \cosh (18 c_1) x^{12}+32 \sinh (18 c_1) x^{12}+40 \cosh (12 c_1) x^6-40 \sinh (12 c_1) x^6+\cosh (6 c_1)-\sinh (6 c_1)+(\cosh (36 c_1)-\sinh (36 c_1)) \sqrt {-4096 \cosh (42 c_1) x^{18}-4096 \sinh (42 c_1) x^{18}+768 \cosh (48 c_1) x^{12}+768 \sinh (48 c_1) x^{12}-48 \cosh (54 c_1) x^6-48 \sinh (54 c_1) x^6+\cosh (60 c_1)+\sinh (60 c_1)}}}{9 x^2}+\frac {4\ 2^{2/3} \left (2 \cosh (12 c_1) x^8+2 \sinh (12 c_1) x^8+\cosh (18 c_1) x^2+\sinh (18 c_1) x^2\right ) (\cosh (24 c_1)-\sinh (24 c_1))}{9 \sqrt [3]{-32 \cosh (18 c_1) x^{12}+32 \sinh (18 c_1) x^{12}+40 \cosh (12 c_1) x^6-40 \sinh (12 c_1) x^6+\cosh (6 c_1)-\sinh (6 c_1)+(\cosh (36 c_1)-\sinh (36 c_1)) \sqrt {-4096 \cosh (42 c_1) x^{18}-4096 \sinh (42 c_1) x^{18}+768 \cosh (48 c_1) x^{12}+768 \sinh (48 c_1) x^{12}-48 \cosh (54 c_1) x^6-48 \sinh (54 c_1) x^6+\cosh (60 c_1)+\sinh (60 c_1)}} x^2}+\frac {1}{81 x^4}}+\frac {1}{2} \sqrt {-\frac {8}{9} \cosh (6 c_1) x^2+\frac {8}{9} \sinh (6 c_1) x^2+\frac {-\frac {128}{27} \cosh (6 c_1)+\frac {128}{27} \sinh (6 c_1)-\frac {8}{729 x^6}}{4 \sqrt {-\frac {4}{9} \cosh (6 c_1) x^2+\frac {4}{9} \sinh (6 c_1) x^2+\frac {\sqrt [3]{2} \sqrt [3]{-32 \cosh (18 c_1) x^{12}+32 \sinh (18 c_1) x^{12}+40 \cosh (12 c_1) x^6-40 \sinh (12 c_1) x^6+\cosh (6 c_1)-\sinh (6 c_1)+(\cosh (36 c_1)-\sinh (36 c_1)) \sqrt {-4096 \cosh (42 c_1) x^{18}-4096 \sinh (42 c_1) x^{18}+768 \cosh (48 c_1) x^{12}+768 \sinh (48 c_1) x^{12}-48 \cosh (54 c_1) x^6-48 \sinh (54 c_1) x^6+\cosh (60 c_1)+\sinh (60 c_1)}}}{9 x^2}+\frac {4\ 2^{2/3} \left (2 \cosh (12 c_1) x^8+2 \sinh (12 c_1) x^8+\cosh (18 c_1) x^2+\sinh (18 c_1) x^2\right ) (\cosh (24 c_1)-\sinh (24 c_1))}{9 \sqrt [3]{-32 \cosh (18 c_1) x^{12}+32 \sinh (18 c_1) x^{12}+40 \cosh (12 c_1) x^6-40 \sinh (12 c_1) x^6+\cosh (6 c_1)-\sinh (6 c_1)+(\cosh (36 c_1)-\sinh (36 c_1)) \sqrt {-4096 \cosh (42 c_1) x^{18}-4096 \sinh (42 c_1) x^{18}+768 \cosh (48 c_1) x^{12}+768 \sinh (48 c_1) x^{12}-48 \cosh (54 c_1) x^6-48 \sinh (54 c_1) x^6+\cosh (60 c_1)+\sinh (60 c_1)}} x^2}+\frac {1}{81 x^4}}}-\frac {\sqrt [3]{2} \sqrt [3]{-32 \cosh (18 c_1) x^{12}+32 \sinh (18 c_1) x^{12}+40 \cosh (12 c_1) x^6-40 \sinh (12 c_1) x^6+\cosh (6 c_1)-\sinh (6 c_1)+(\cosh (36 c_1)-\sinh (36 c_1)) \sqrt {-4096 \cosh (42 c_1) x^{18}-4096 \sinh (42 c_1) x^{18}+768 \cosh (48 c_1) x^{12}+768 \sinh (48 c_1) x^{12}-48 \cosh (54 c_1) x^6-48 \sinh (54 c_1) x^6+\cosh (60 c_1)+\sinh (60 c_1)}}}{9 x^2}-\frac {4\ 2^{2/3} \left (2 \cosh (12 c_1) x^8+2 \sinh (12 c_1) x^8+\cosh (18 c_1) x^2+\sinh (18 c_1) x^2\right ) (\cosh (24 c_1)-\sinh (24 c_1))}{9 \sqrt [3]{-32 \cosh (18 c_1) x^{12}+32 \sinh (18 c_1) x^{12}+40 \cosh (12 c_1) x^6-40 \sinh (12 c_1) x^6+\cosh (6 c_1)-\sinh (6 c_1)+(\cosh (36 c_1)-\sinh (36 c_1)) \sqrt {-4096 \cosh (42 c_1) x^{18}-4096 \sinh (42 c_1) x^{18}+768 \cosh (48 c_1) x^{12}+768 \sinh (48 c_1) x^{12}-48 \cosh (54 c_1) x^6-48 \sinh (54 c_1) x^6+\cosh (60 c_1)+\sinh (60 c_1)}} x^2}+\frac {2}{81 x^4}}-\frac {1}{18 x^2}\right \},\left \{y(x)\to -\frac {1}{2} \sqrt {\frac {4}{9} \cosh (6 c_1) x^2-\frac {4}{9} \sinh (6 c_1) x^2+\frac {\sqrt [3]{2} \sqrt [3]{32 \cosh (18 c_1) x^{12}-32 \sinh (18 c_1) x^{12}+40 \cosh (12 c_1) x^6-40 \sinh (12 c_1) x^6-\cosh (6 c_1)+\sinh (6 c_1)+(\cosh (36 c_1)-\sinh (36 c_1)) \sqrt {4096 \cosh (42 c_1) x^{18}+4096 \sinh (42 c_1) x^{18}+768 \cosh (48 c_1) x^{12}+768 \sinh (48 c_1) x^{12}+48 \cosh (54 c_1) x^6+48 \sinh (54 c_1) x^6+\cosh (60 c_1)+\sinh (60 c_1)}}}{9 x^2}+\frac {4\ 2^{2/3} \left (2 \cosh (12 c_1) x^8+2 \sinh (12 c_1) x^8-\cosh (18 c_1) x^2-\sinh (18 c_1) x^2\right ) (\cosh (24 c_1)-\sinh (24 c_1))}{9 \sqrt [3]{32 \cosh (18 c_1) x^{12}-32 \sinh (18 c_1) x^{12}+40 \cosh (12 c_1) x^6-40 \sinh (12 c_1) x^6-\cosh (6 c_1)+\sinh (6 c_1)+(\cosh (36 c_1)-\sinh (36 c_1)) \sqrt {4096 \cosh (42 c_1) x^{18}+4096 \sinh (42 c_1) x^{18}+768 \cosh (48 c_1) x^{12}+768 \sinh (48 c_1) x^{12}+48 \cosh (54 c_1) x^6+48 \sinh (54 c_1) x^6+\cosh (60 c_1)+\sinh (60 c_1)}} x^2}+\frac {1}{81 x^4}}-\frac {1}{2} \sqrt {\frac {8}{9} \cosh (6 c_1) x^2-\frac {8}{9} \sinh (6 c_1) x^2-\frac {\frac {128}{27} \cosh (6 c_1)-\frac {128}{27} \sinh (6 c_1)-\frac {8}{729 x^6}}{4 \sqrt {\frac {4}{9} \cosh (6 c_1) x^2-\frac {4}{9} \sinh (6 c_1) x^2+\frac {\sqrt [3]{2} \sqrt [3]{32 \cosh (18 c_1) x^{12}-32 \sinh (18 c_1) x^{12}+40 \cosh (12 c_1) x^6-40 \sinh (12 c_1) x^6-\cosh (6 c_1)+\sinh (6 c_1)+(\cosh (36 c_1)-\sinh (36 c_1)) \sqrt {4096 \cosh (42 c_1) x^{18}+4096 \sinh (42 c_1) x^{18}+768 \cosh (48 c_1) x^{12}+768 \sinh (48 c_1) x^{12}+48 \cosh (54 c_1) x^6+48 \sinh (54 c_1) x^6+\cosh (60 c_1)+\sinh (60 c_1)}}}{9 x^2}+\frac {4\ 2^{2/3} \left (2 \cosh (12 c_1) x^8+2 \sinh (12 c_1) x^8-\cosh (18 c_1) x^2-\sinh (18 c_1) x^2\right ) (\cosh (24 c_1)-\sinh (24 c_1))}{9 \sqrt [3]{32 \cosh (18 c_1) x^{12}-32 \sinh (18 c_1) x^{12}+40 \cosh (12 c_1) x^6-40 \sinh (12 c_1) x^6-\cosh (6 c_1)+\sinh (6 c_1)+(\cosh (36 c_1)-\sinh (36 c_1)) \sqrt {4096 \cosh (42 c_1) x^{18}+4096 \sinh (42 c_1) x^{18}+768 \cosh (48 c_1) x^{12}+768 \sinh (48 c_1) x^{12}+48 \cosh (54 c_1) x^6+48 \sinh (54 c_1) x^6+\cosh (60 c_1)+\sinh (60 c_1)}} x^2}+\frac {1}{81 x^4}}}-\frac {\sqrt [3]{2} \sqrt [3]{32 \cosh (18 c_1) x^{12}-32 \sinh (18 c_1) x^{12}+40 \cosh (12 c_1) x^6-40 \sinh (12 c_1) x^6-\cosh (6 c_1)+\sinh (6 c_1)+(\cosh (36 c_1)-\sinh (36 c_1)) \sqrt {4096 \cosh (42 c_1) x^{18}+4096 \sinh (42 c_1) x^{18}+768 \cosh (48 c_1) x^{12}+768 \sinh (48 c_1) x^{12}+48 \cosh (54 c_1) x^6+48 \sinh (54 c_1) x^6+\cosh (60 c_1)+\sinh (60 c_1)}}}{9 x^2}-\frac {4\ 2^{2/3} \left (2 \cosh (12 c_1) x^8+2 \sinh (12 c_1) x^8-\cosh (18 c_1) x^2-\sinh (18 c_1) x^2\right ) (\cosh (24 c_1)-\sinh (24 c_1))}{9 \sqrt [3]{32 \cosh (18 c_1) x^{12}-32 \sinh (18 c_1) x^{12}+40 \cosh (12 c_1) x^6-40 \sinh (12 c_1) x^6-\cosh (6 c_1)+\sinh (6 c_1)+(\cosh (36 c_1)-\sinh (36 c_1)) \sqrt {4096 \cosh (42 c_1) x^{18}+4096 \sinh (42 c_1) x^{18}+768 \cosh (48 c_1) x^{12}+768 \sinh (48 c_1) x^{12}+48 \cosh (54 c_1) x^6+48 \sinh (54 c_1) x^6+\cosh (60 c_1)+\sinh (60 c_1)}} x^2}+\frac {2}{81 x^4}}-\frac {1}{18 x^2}\right \},\left \{y(x)\to -\frac {1}{2} \sqrt {\frac {4}{9} \cosh (6 c_1) x^2-\frac {4}{9} \sinh (6 c_1) x^2+\frac {\sqrt [3]{2} \sqrt [3]{32 \cosh (18 c_1) x^{12}-32 \sinh (18 c_1) x^{12}+40 \cosh (12 c_1) x^6-40 \sinh (12 c_1) x^6-\cosh (6 c_1)+\sinh (6 c_1)+(\cosh (36 c_1)-\sinh (36 c_1)) \sqrt {4096 \cosh (42 c_1) x^{18}+4096 \sinh (42 c_1) x^{18}+768 \cosh (48 c_1) x^{12}+768 \sinh (48 c_1) x^{12}+48 \cosh (54 c_1) x^6+48 \sinh (54 c_1) x^6+\cosh (60 c_1)+\sinh (60 c_1)}}}{9 x^2}+\frac {4\ 2^{2/3} \left (2 \cosh (12 c_1) x^8+2 \sinh (12 c_1) x^8-\cosh (18 c_1) x^2-\sinh (18 c_1) x^2\right ) (\cosh (24 c_1)-\sinh (24 c_1))}{9 \sqrt [3]{32 \cosh (18 c_1) x^{12}-32 \sinh (18 c_1) x^{12}+40 \cosh (12 c_1) x^6-40 \sinh (12 c_1) x^6-\cosh (6 c_1)+\sinh (6 c_1)+(\cosh (36 c_1)-\sinh (36 c_1)) \sqrt {4096 \cosh (42 c_1) x^{18}+4096 \sinh (42 c_1) x^{18}+768 \cosh (48 c_1) x^{12}+768 \sinh (48 c_1) x^{12}+48 \cosh (54 c_1) x^6+48 \sinh (54 c_1) x^6+\cosh (60 c_1)+\sinh (60 c_1)}} x^2}+\frac {1}{81 x^4}}+\frac {1}{2} \sqrt {\frac {8}{9} \cosh (6 c_1) x^2-\frac {8}{9} \sinh (6 c_1) x^2-\frac {\frac {128}{27} \cosh (6 c_1)-\frac {128}{27} \sinh (6 c_1)-\frac {8}{729 x^6}}{4 \sqrt {\frac {4}{9} \cosh (6 c_1) x^2-\frac {4}{9} \sinh (6 c_1) x^2+\frac {\sqrt [3]{2} \sqrt [3]{32 \cosh (18 c_1) x^{12}-32 \sinh (18 c_1) x^{12}+40 \cosh (12 c_1) x^6-40 \sinh (12 c_1) x^6-\cosh (6 c_1)+\sinh (6 c_1)+(\cosh (36 c_1)-\sinh (36 c_1)) \sqrt {4096 \cosh (42 c_1) x^{18}+4096 \sinh (42 c_1) x^{18}+768 \cosh (48 c_1) x^{12}+768 \sinh (48 c_1) x^{12}+48 \cosh (54 c_1) x^6+48 \sinh (54 c_1) x^6+\cosh (60 c_1)+\sinh (60 c_1)}}}{9 x^2}+\frac {4\ 2^{2/3} \left (2 \cosh (12 c_1) x^8+2 \sinh (12 c_1) x^8-\cosh (18 c_1) x^2-\sinh (18 c_1) x^2\right ) (\cosh (24 c_1)-\sinh (24 c_1))}{9 \sqrt [3]{32 \cosh (18 c_1) x^{12}-32 \sinh (18 c_1) x^{12}+40 \cosh (12 c_1) x^6-40 \sinh (12 c_1) x^6-\cosh (6 c_1)+\sinh (6 c_1)+(\cosh (36 c_1)-\sinh (36 c_1)) \sqrt {4096 \cosh (42 c_1) x^{18}+4096 \sinh (42 c_1) x^{18}+768 \cosh (48 c_1) x^{12}+768 \sinh (48 c_1) x^{12}+48 \cosh (54 c_1) x^6+48 \sinh (54 c_1) x^6+\cosh (60 c_1)+\sinh (60 c_1)}} x^2}+\frac {1}{81 x^4}}}-\frac {\sqrt [3]{2} \sqrt [3]{32 \cosh (18 c_1) x^{12}-32 \sinh (18 c_1) x^{12}+40 \cosh (12 c_1) x^6-40 \sinh (12 c_1) x^6-\cosh (6 c_1)+\sinh (6 c_1)+(\cosh (36 c_1)-\sinh (36 c_1)) \sqrt {4096 \cosh (42 c_1) x^{18}+4096 \sinh (42 c_1) x^{18}+768 \cosh (48 c_1) x^{12}+768 \sinh (48 c_1) x^{12}+48 \cosh (54 c_1) x^6+48 \sinh (54 c_1) x^6+\cosh (60 c_1)+\sinh (60 c_1)}}}{9 x^2}-\frac {4\ 2^{2/3} \left (2 \cosh (12 c_1) x^8+2 \sinh (12 c_1) x^8-\cosh (18 c_1) x^2-\sinh (18 c_1) x^2\right ) (\cosh (24 c_1)-\sinh (24 c_1))}{9 \sqrt [3]{32 \cosh (18 c_1) x^{12}-32 \sinh (18 c_1) x^{12}+40 \cosh (12 c_1) x^6-40 \sinh (12 c_1) x^6-\cosh (6 c_1)+\sinh (6 c_1)+(\cosh (36 c_1)-\sinh (36 c_1)) \sqrt {4096 \cosh (42 c_1) x^{18}+4096 \sinh (42 c_1) x^{18}+768 \cosh (48 c_1) x^{12}+768 \sinh (48 c_1) x^{12}+48 \cosh (54 c_1) x^6+48 \sinh (54 c_1) x^6+\cosh (60 c_1)+\sinh (60 c_1)}} x^2}+\frac {2}{81 x^4}}-\frac {1}{18 x^2}\right \},\left \{y(x)\to \frac {1}{2} \sqrt {\frac {4}{9} \cosh (6 c_1) x^2-\frac {4}{9} \sinh (6 c_1) x^2+\frac {\sqrt [3]{2} \sqrt [3]{32 \cosh (18 c_1) x^{12}-32 \sinh (18 c_1) x^{12}+40 \cosh (12 c_1) x^6-40 \sinh (12 c_1) x^6-\cosh (6 c_1)+\sinh (6 c_1)+(\cosh (36 c_1)-\sinh (36 c_1)) \sqrt {4096 \cosh (42 c_1) x^{18}+4096 \sinh (42 c_1) x^{18}+768 \cosh (48 c_1) x^{12}+768 \sinh (48 c_1) x^{12}+48 \cosh (54 c_1) x^6+48 \sinh (54 c_1) x^6+\cosh (60 c_1)+\sinh (60 c_1)}}}{9 x^2}+\frac {4\ 2^{2/3} \left (2 \cosh (12 c_1) x^8+2 \sinh (12 c_1) x^8-\cosh (18 c_1) x^2-\sinh (18 c_1) x^2\right ) (\cosh (24 c_1)-\sinh (24 c_1))}{9 \sqrt [3]{32 \cosh (18 c_1) x^{12}-32 \sinh (18 c_1) x^{12}+40 \cosh (12 c_1) x^6-40 \sinh (12 c_1) x^6-\cosh (6 c_1)+\sinh (6 c_1)+(\cosh (36 c_1)-\sinh (36 c_1)) \sqrt {4096 \cosh (42 c_1) x^{18}+4096 \sinh (42 c_1) x^{18}+768 \cosh (48 c_1) x^{12}+768 \sinh (48 c_1) x^{12}+48 \cosh (54 c_1) x^6+48 \sinh (54 c_1) x^6+\cosh (60 c_1)+\sinh (60 c_1)}} x^2}+\frac {1}{81 x^4}}-\frac {1}{2} \sqrt {\frac {8}{9} \cosh (6 c_1) x^2-\frac {8}{9} \sinh (6 c_1) x^2+\frac {\frac {128}{27} \cosh (6 c_1)-\frac {128}{27} \sinh (6 c_1)-\frac {8}{729 x^6}}{4 \sqrt {\frac {4}{9} \cosh (6 c_1) x^2-\frac {4}{9} \sinh (6 c_1) x^2+\frac {\sqrt [3]{2} \sqrt [3]{32 \cosh (18 c_1) x^{12}-32 \sinh (18 c_1) x^{12}+40 \cosh (12 c_1) x^6-40 \sinh (12 c_1) x^6-\cosh (6 c_1)+\sinh (6 c_1)+(\cosh (36 c_1)-\sinh (36 c_1)) \sqrt {4096 \cosh (42 c_1) x^{18}+4096 \sinh (42 c_1) x^{18}+768 \cosh (48 c_1) x^{12}+768 \sinh (48 c_1) x^{12}+48 \cosh (54 c_1) x^6+48 \sinh (54 c_1) x^6+\cosh (60 c_1)+\sinh (60 c_1)}}}{9 x^2}+\frac {4\ 2^{2/3} \left (2 \cosh (12 c_1) x^8+2 \sinh (12 c_1) x^8-\cosh (18 c_1) x^2-\sinh (18 c_1) x^2\right ) (\cosh (24 c_1)-\sinh (24 c_1))}{9 \sqrt [3]{32 \cosh (18 c_1) x^{12}-32 \sinh (18 c_1) x^{12}+40 \cosh (12 c_1) x^6-40 \sinh (12 c_1) x^6-\cosh (6 c_1)+\sinh (6 c_1)+(\cosh (36 c_1)-\sinh (36 c_1)) \sqrt {4096 \cosh (42 c_1) x^{18}+4096 \sinh (42 c_1) x^{18}+768 \cosh (48 c_1) x^{12}+768 \sinh (48 c_1) x^{12}+48 \cosh (54 c_1) x^6+48 \sinh (54 c_1) x^6+\cosh (60 c_1)+\sinh (60 c_1)}} x^2}+\frac {1}{81 x^4}}}-\frac {\sqrt [3]{2} \sqrt [3]{32 \cosh (18 c_1) x^{12}-32 \sinh (18 c_1) x^{12}+40 \cosh (12 c_1) x^6-40 \sinh (12 c_1) x^6-\cosh (6 c_1)+\sinh (6 c_1)+(\cosh (36 c_1)-\sinh (36 c_1)) \sqrt {4096 \cosh (42 c_1) x^{18}+4096 \sinh (42 c_1) x^{18}+768 \cosh (48 c_1) x^{12}+768 \sinh (48 c_1) x^{12}+48 \cosh (54 c_1) x^6+48 \sinh (54 c_1) x^6+\cosh (60 c_1)+\sinh (60 c_1)}}}{9 x^2}-\frac {4\ 2^{2/3} \left (2 \cosh (12 c_1) x^8+2 \sinh (12 c_1) x^8-\cosh (18 c_1) x^2-\sinh (18 c_1) x^2\right ) (\cosh (24 c_1)-\sinh (24 c_1))}{9 \sqrt [3]{32 \cosh (18 c_1) x^{12}-32 \sinh (18 c_1) x^{12}+40 \cosh (12 c_1) x^6-40 \sinh (12 c_1) x^6-\cosh (6 c_1)+\sinh (6 c_1)+(\cosh (36 c_1)-\sinh (36 c_1)) \sqrt {4096 \cosh (42 c_1) x^{18}+4096 \sinh (42 c_1) x^{18}+768 \cosh (48 c_1) x^{12}+768 \sinh (48 c_1) x^{12}+48 \cosh (54 c_1) x^6+48 \sinh (54 c_1) x^6+\cosh (60 c_1)+\sinh (60 c_1)}} x^2}+\frac {2}{81 x^4}}-\frac {1}{18 x^2}\right \},\left \{y(x)\to \frac {1}{2} \sqrt {\frac {4}{9} \cosh (6 c_1) x^2-\frac {4}{9} \sinh (6 c_1) x^2+\frac {\sqrt [3]{2} \sqrt [3]{32 \cosh (18 c_1) x^{12}-32 \sinh (18 c_1) x^{12}+40 \cosh (12 c_1) x^6-40 \sinh (12 c_1) x^6-\cosh (6 c_1)+\sinh (6 c_1)+(\cosh (36 c_1)-\sinh (36 c_1)) \sqrt {4096 \cosh (42 c_1) x^{18}+4096 \sinh (42 c_1) x^{18}+768 \cosh (48 c_1) x^{12}+768 \sinh (48 c_1) x^{12}+48 \cosh (54 c_1) x^6+48 \sinh (54 c_1) x^6+\cosh (60 c_1)+\sinh (60 c_1)}}}{9 x^2}+\frac {4\ 2^{2/3} \left (2 \cosh (12 c_1) x^8+2 \sinh (12 c_1) x^8-\cosh (18 c_1) x^2-\sinh (18 c_1) x^2\right ) (\cosh (24 c_1)-\sinh (24 c_1))}{9 \sqrt [3]{32 \cosh (18 c_1) x^{12}-32 \sinh (18 c_1) x^{12}+40 \cosh (12 c_1) x^6-40 \sinh (12 c_1) x^6-\cosh (6 c_1)+\sinh (6 c_1)+(\cosh (36 c_1)-\sinh (36 c_1)) \sqrt {4096 \cosh (42 c_1) x^{18}+4096 \sinh (42 c_1) x^{18}+768 \cosh (48 c_1) x^{12}+768 \sinh (48 c_1) x^{12}+48 \cosh (54 c_1) x^6+48 \sinh (54 c_1) x^6+\cosh (60 c_1)+\sinh (60 c_1)}} x^2}+\frac {1}{81 x^4}}+\frac {1}{2} \sqrt {\frac {8}{9} \cosh (6 c_1) x^2-\frac {8}{9} \sinh (6 c_1) x^2+\frac {\frac {128}{27} \cosh (6 c_1)-\frac {128}{27} \sinh (6 c_1)-\frac {8}{729 x^6}}{4 \sqrt {\frac {4}{9} \cosh (6 c_1) x^2-\frac {4}{9} \sinh (6 c_1) x^2+\frac {\sqrt [3]{2} \sqrt [3]{32 \cosh (18 c_1) x^{12}-32 \sinh (18 c_1) x^{12}+40 \cosh (12 c_1) x^6-40 \sinh (12 c_1) x^6-\cosh (6 c_1)+\sinh (6 c_1)+(\cosh (36 c_1)-\sinh (36 c_1)) \sqrt {4096 \cosh (42 c_1) x^{18}+4096 \sinh (42 c_1) x^{18}+768 \cosh (48 c_1) x^{12}+768 \sinh (48 c_1) x^{12}+48 \cosh (54 c_1) x^6+48 \sinh (54 c_1) x^6+\cosh (60 c_1)+\sinh (60 c_1)}}}{9 x^2}+\frac {4\ 2^{2/3} \left (2 \cosh (12 c_1) x^8+2 \sinh (12 c_1) x^8-\cosh (18 c_1) x^2-\sinh (18 c_1) x^2\right ) (\cosh (24 c_1)-\sinh (24 c_1))}{9 \sqrt [3]{32 \cosh (18 c_1) x^{12}-32 \sinh (18 c_1) x^{12}+40 \cosh (12 c_1) x^6-40 \sinh (12 c_1) x^6-\cosh (6 c_1)+\sinh (6 c_1)+(\cosh (36 c_1)-\sinh (36 c_1)) \sqrt {4096 \cosh (42 c_1) x^{18}+4096 \sinh (42 c_1) x^{18}+768 \cosh (48 c_1) x^{12}+768 \sinh (48 c_1) x^{12}+48 \cosh (54 c_1) x^6+48 \sinh (54 c_1) x^6+\cosh (60 c_1)+\sinh (60 c_1)}} x^2}+\frac {1}{81 x^4}}}-\frac {\sqrt [3]{2} \sqrt [3]{32 \cosh (18 c_1) x^{12}-32 \sinh (18 c_1) x^{12}+40 \cosh (12 c_1) x^6-40 \sinh (12 c_1) x^6-\cosh (6 c_1)+\sinh (6 c_1)+(\cosh (36 c_1)-\sinh (36 c_1)) \sqrt {4096 \cosh (42 c_1) x^{18}+4096 \sinh (42 c_1) x^{18}+768 \cosh (48 c_1) x^{12}+768 \sinh (48 c_1) x^{12}+48 \cosh (54 c_1) x^6+48 \sinh (54 c_1) x^6+\cosh (60 c_1)+\sinh (60 c_1)}}}{9 x^2}-\frac {4\ 2^{2/3} \left (2 \cosh (12 c_1) x^8+2 \sinh (12 c_1) x^8-\cosh (18 c_1) x^2-\sinh (18 c_1) x^2\right ) (\cosh (24 c_1)-\sinh (24 c_1))}{9 \sqrt [3]{32 \cosh (18 c_1) x^{12}-32 \sinh (18 c_1) x^{12}+40 \cosh (12 c_1) x^6-40 \sinh (12 c_1) x^6-\cosh (6 c_1)+\sinh (6 c_1)+(\cosh (36 c_1)-\sinh (36 c_1)) \sqrt {4096 \cosh (42 c_1) x^{18}+4096 \sinh (42 c_1) x^{18}+768 \cosh (48 c_1) x^{12}+768 \sinh (48 c_1) x^{12}+48 \cosh (54 c_1) x^6+48 \sinh (54 c_1) x^6+\cosh (60 c_1)+\sinh (60 c_1)}} x^2}+\frac {2}{81 x^4}}-\frac {1}{18 x^2}\right \}\right \}$ Maple : cpu = 7.904 (sec), leaf count = 221

$\left \{ y \left ( x \right ) =-{\frac {2}{9\,{x}^{2}}},y \left ( x \right ) ={\frac { \left ( {\it RootOf} \left ( -729\,{\it \_C1}\,{x}^{12}+{{\it \_Z}}^{8}-12\,{{\it \_Z}}^{7}+60\,{{\it \_Z}}^{6}-160\,{{\it \_Z}}^{5}+240\,{{\it \_Z}}^{4}-192\,{{\it \_Z}}^{3}+64\,{{\it \_Z}}^{2} \right ) -2 \right ) \left ( {\it RootOf} \left ( -729\,{\it \_C1}\,{x}^{12}+{{\it \_Z}}^{8}-12\,{{\it \_Z}}^{7}+60\,{{\it \_Z}}^{6}-160\,{{\it \_Z}}^{5}+240\,{{\it \_Z}}^{4}-192\,{{\it \_Z}}^{3}+64\,{{\it \_Z}}^{2} \right ) +1 \right ) }{9\,{x}^{2}}},y \left ( x \right ) ={\frac { \left ( {\it RootOf} \left ( -729\,{x}^{12}+{\it \_C1}\,{{\it \_Z}}^{8}+4\,{\it \_C1}\,{{\it \_Z}}^{7}+4\,{\it \_C1}\,{{\it \_Z}}^{6}-4\,{\it \_C1}\,{{\it \_Z}}^{5}-10\,{\it \_C1}\,{{\it \_Z}}^{4}-4\,{\it \_C1}\,{{\it \_Z}}^{3}+4\,{{\it \_Z}}^{2}{\it \_C1}+4\,{\it \_Z}\,{\it \_C1}+{\it \_C1} \right ) -2 \right ) \left ( {\it RootOf} \left ( -729\,{x}^{12}+{\it \_C1}\,{{\it \_Z}}^{8}+4\,{\it \_C1}\,{{\it \_Z}}^{7}+4\,{\it \_C1}\,{{\it \_Z}}^{6}-4\,{\it \_C1}\,{{\it \_Z}}^{5}-10\,{\it \_C1}\,{{\it \_Z}}^{4}-4\,{\it \_C1}\,{{\it \_Z}}^{3}+4\,{{\it \_Z}}^{2}{\it \_C1}+4\,{\it \_Z}\,{\it \_C1}+{\it \_C1} \right ) +1 \right ) }{9\,{x}^{2}}} \right \}$