\[ a+x y'(x)^2+y(x) y'(x)=0 \] ✓ Mathematica : cpu = 27.581 (sec), leaf count = 16145
\[\left \{\left \{y(x)\to -\sqrt {-\frac {4 a x}{3}-\frac {1}{2} \sqrt {-\frac {64}{9} a^2 x^2+\frac {\cosh \left (3 c_1\right )}{81 a x}+\frac {\sinh \left (3 c_1\right )}{81 a x}+\frac {\sqrt [3]{4529848320 a^6 \cosh \left (6 c_1\right ) x^6+4529848320 a^6 \sinh \left (6 c_1\right ) x^6+1105920 a^3 \cosh \left (9 c_1\right ) x^3+1105920 a^3 \sinh \left (9 c_1\right ) x^3+432 \cosh \left (12 c_1\right )+432 \sinh \left (12 c_1\right )+\sqrt {-3361919107433565782016 a^{15} \cosh \left (9 c_1\right ) x^{15}-3361919107433565782016 a^{15} \sinh \left (9 c_1\right ) x^{15}+8207810320882728960 a^{12} \cosh \left (12 c_1\right ) x^{12}+8207810320882728960 a^{12} \sinh \left (12 c_1\right ) x^{12}-5009649854054400 a^9 \cosh \left (15 c_1\right ) x^9-5009649854054400 a^9 \sinh \left (15 c_1\right ) x^9-978447237120 a^6 \cosh \left (18 c_1\right ) x^6-978447237120 a^6 \sinh \left (18 c_1\right ) x^6+955514880 a^3 \cosh \left (21 c_1\right ) x^3+955514880 a^3 \sinh \left (21 c_1\right ) x^3+186624 \cosh \left (24 c_1\right )+186624 \sinh \left (24 c_1\right )}}}{3888 \sqrt [3]{2} a^2 x^2}+\frac {16 \sqrt [3]{2} \left (4096 a^5 \cosh \left (3 c_1\right ) x^5+4096 a^5 \sinh \left (3 c_1\right ) x^5+5 a^2 \cosh \left (6 c_1\right ) x^2+5 a^2 \sinh \left (6 c_1\right ) x^2\right )}{27 a^2 \sqrt [3]{4529848320 a^6 \cosh \left (6 c_1\right ) x^6+4529848320 a^6 \sinh \left (6 c_1\right ) x^6+1105920 a^3 \cosh \left (9 c_1\right ) x^3+1105920 a^3 \sinh \left (9 c_1\right ) x^3+432 \cosh \left (12 c_1\right )+432 \sinh \left (12 c_1\right )+\sqrt {-3361919107433565782016 a^{15} \cosh \left (9 c_1\right ) x^{15}-3361919107433565782016 a^{15} \sinh \left (9 c_1\right ) x^{15}+8207810320882728960 a^{12} \cosh \left (12 c_1\right ) x^{12}+8207810320882728960 a^{12} \sinh \left (12 c_1\right ) x^{12}-5009649854054400 a^9 \cosh \left (15 c_1\right ) x^9-5009649854054400 a^9 \sinh \left (15 c_1\right ) x^9-978447237120 a^6 \cosh \left (18 c_1\right ) x^6-978447237120 a^6 \sinh \left (18 c_1\right ) x^6+955514880 a^3 \cosh \left (21 c_1\right ) x^3+955514880 a^3 \sinh \left (21 c_1\right ) x^3+186624 \cosh \left (24 c_1\right )+186624 \sinh \left (24 c_1\right )}} x^2}+\frac {\left (1728 a^3 x^3-\cosh \left (3 c_1\right )-\sinh \left (3 c_1\right )\right ){}^2}{419904 a^4 x^4}}-\frac {1}{2} \sqrt {-\frac {128}{9} a^2 x^2-\frac {\frac {\cosh ^3\left (3 c_1\right )}{34012224 a^6 x^6}+\frac {\sinh \left (3 c_1\right ) \cosh ^2\left (3 c_1\right )}{11337408 a^6 x^6}+\frac {\cosh ^2\left (3 c_1\right )}{13122 a^3 x^3}+\frac {\sinh ^2\left (3 c_1\right ) \cosh \left (3 c_1\right )}{11337408 a^6 x^6}+\frac {\sinh \left (3 c_1\right ) \cosh \left (3 c_1\right )}{6561 a^3 x^3}+\frac {512}{243} \cosh \left (3 c_1\right )+\frac {\sinh ^3\left (3 c_1\right )}{34012224 a^6 x^6}+\frac {\sinh ^2\left (3 c_1\right )}{13122 a^3 x^3}+\frac {512}{243} \sinh \left (3 c_1\right )}{4 \sqrt {-\frac {64}{9} a^2 x^2+\frac {\cosh \left (3 c_1\right )}{81 a x}+\frac {\sinh \left (3 c_1\right )}{81 a x}+\frac {\sqrt [3]{4529848320 a^6 \cosh \left (6 c_1\right ) x^6+4529848320 a^6 \sinh \left (6 c_1\right ) x^6+1105920 a^3 \cosh \left (9 c_1\right ) x^3+1105920 a^3 \sinh \left (9 c_1\right ) x^3+432 \cosh \left (12 c_1\right )+432 \sinh \left (12 c_1\right )+\sqrt {-3361919107433565782016 a^{15} \cosh \left (9 c_1\right ) x^{15}-3361919107433565782016 a^{15} \sinh \left (9 c_1\right ) x^{15}+8207810320882728960 a^{12} \cosh \left (12 c_1\right ) x^{12}+8207810320882728960 a^{12} \sinh \left (12 c_1\right ) x^{12}-5009649854054400 a^9 \cosh \left (15 c_1\right ) x^9-5009649854054400 a^9 \sinh \left (15 c_1\right ) x^9-978447237120 a^6 \cosh \left (18 c_1\right ) x^6-978447237120 a^6 \sinh \left (18 c_1\right ) x^6+955514880 a^3 \cosh \left (21 c_1\right ) x^3+955514880 a^3 \sinh \left (21 c_1\right ) x^3+186624 \cosh \left (24 c_1\right )+186624 \sinh \left (24 c_1\right )}}}{3888 \sqrt [3]{2} a^2 x^2}+\frac {16 \sqrt [3]{2} \left (4096 a^5 \cosh \left (3 c_1\right ) x^5+4096 a^5 \sinh \left (3 c_1\right ) x^5+5 a^2 \cosh \left (6 c_1\right ) x^2+5 a^2 \sinh \left (6 c_1\right ) x^2\right )}{27 a^2 \sqrt [3]{4529848320 a^6 \cosh \left (6 c_1\right ) x^6+4529848320 a^6 \sinh \left (6 c_1\right ) x^6+1105920 a^3 \cosh \left (9 c_1\right ) x^3+1105920 a^3 \sinh \left (9 c_1\right ) x^3+432 \cosh \left (12 c_1\right )+432 \sinh \left (12 c_1\right )+\sqrt {-3361919107433565782016 a^{15} \cosh \left (9 c_1\right ) x^{15}-3361919107433565782016 a^{15} \sinh \left (9 c_1\right ) x^{15}+8207810320882728960 a^{12} \cosh \left (12 c_1\right ) x^{12}+8207810320882728960 a^{12} \sinh \left (12 c_1\right ) x^{12}-5009649854054400 a^9 \cosh \left (15 c_1\right ) x^9-5009649854054400 a^9 \sinh \left (15 c_1\right ) x^9-978447237120 a^6 \cosh \left (18 c_1\right ) x^6-978447237120 a^6 \sinh \left (18 c_1\right ) x^6+955514880 a^3 \cosh \left (21 c_1\right ) x^3+955514880 a^3 \sinh \left (21 c_1\right ) x^3+186624 \cosh \left (24 c_1\right )+186624 \sinh \left (24 c_1\right )}} x^2}+\frac {\left (1728 a^3 x^3-\cosh \left (3 c_1\right )-\sinh \left (3 c_1\right )\right ){}^2}{419904 a^4 x^4}}}+\frac {2 \cosh \left (3 c_1\right )}{81 a x}+\frac {2 \sinh \left (3 c_1\right )}{81 a x}-\frac {\sqrt [3]{4529848320 a^6 \cosh \left (6 c_1\right ) x^6+4529848320 a^6 \sinh \left (6 c_1\right ) x^6+1105920 a^3 \cosh \left (9 c_1\right ) x^3+1105920 a^3 \sinh \left (9 c_1\right ) x^3+432 \cosh \left (12 c_1\right )+432 \sinh \left (12 c_1\right )+\sqrt {-3361919107433565782016 a^{15} \cosh \left (9 c_1\right ) x^{15}-3361919107433565782016 a^{15} \sinh \left (9 c_1\right ) x^{15}+8207810320882728960 a^{12} \cosh \left (12 c_1\right ) x^{12}+8207810320882728960 a^{12} \sinh \left (12 c_1\right ) x^{12}-5009649854054400 a^9 \cosh \left (15 c_1\right ) x^9-5009649854054400 a^9 \sinh \left (15 c_1\right ) x^9-978447237120 a^6 \cosh \left (18 c_1\right ) x^6-978447237120 a^6 \sinh \left (18 c_1\right ) x^6+955514880 a^3 \cosh \left (21 c_1\right ) x^3+955514880 a^3 \sinh \left (21 c_1\right ) x^3+186624 \cosh \left (24 c_1\right )+186624 \sinh \left (24 c_1\right )}}}{3888 \sqrt [3]{2} a^2 x^2}-\frac {16 \sqrt [3]{2} \left (4096 a^5 \cosh \left (3 c_1\right ) x^5+4096 a^5 \sinh \left (3 c_1\right ) x^5+5 a^2 \cosh \left (6 c_1\right ) x^2+5 a^2 \sinh \left (6 c_1\right ) x^2\right )}{27 a^2 \sqrt [3]{4529848320 a^6 \cosh \left (6 c_1\right ) x^6+4529848320 a^6 \sinh \left (6 c_1\right ) x^6+1105920 a^3 \cosh \left (9 c_1\right ) x^3+1105920 a^3 \sinh \left (9 c_1\right ) x^3+432 \cosh \left (12 c_1\right )+432 \sinh \left (12 c_1\right )+\sqrt {-3361919107433565782016 a^{15} \cosh \left (9 c_1\right ) x^{15}-3361919107433565782016 a^{15} \sinh \left (9 c_1\right ) x^{15}+8207810320882728960 a^{12} \cosh \left (12 c_1\right ) x^{12}+8207810320882728960 a^{12} \sinh \left (12 c_1\right ) x^{12}-5009649854054400 a^9 \cosh \left (15 c_1\right ) x^9-5009649854054400 a^9 \sinh \left (15 c_1\right ) x^9-978447237120 a^6 \cosh \left (18 c_1\right ) x^6-978447237120 a^6 \sinh \left (18 c_1\right ) x^6+955514880 a^3 \cosh \left (21 c_1\right ) x^3+955514880 a^3 \sinh \left (21 c_1\right ) x^3+186624 \cosh \left (24 c_1\right )+186624 \sinh \left (24 c_1\right )}} x^2}+\frac {\left (1728 a^3 x^3-\cosh \left (3 c_1\right )-\sinh \left (3 c_1\right )\right ){}^2}{209952 a^4 x^4}}+\frac {\cosh \left (3 c_1\right )}{1296 a^2 x^2}+\frac {\sinh \left (3 c_1\right )}{1296 a^2 x^2}}\right \},\left \{y(x)\to \sqrt {-\frac {4 a x}{3}-\frac {1}{2} \sqrt {-\frac {64}{9} a^2 x^2+\frac {\cosh \left (3 c_1\right )}{81 a x}+\frac {\sinh \left (3 c_1\right )}{81 a x}+\frac {\sqrt [3]{4529848320 a^6 \cosh \left (6 c_1\right ) x^6+4529848320 a^6 \sinh \left (6 c_1\right ) x^6+1105920 a^3 \cosh \left (9 c_1\right ) x^3+1105920 a^3 \sinh \left (9 c_1\right ) x^3+432 \cosh \left (12 c_1\right )+432 \sinh \left (12 c_1\right )+\sqrt {-3361919107433565782016 a^{15} \cosh \left (9 c_1\right ) x^{15}-3361919107433565782016 a^{15} \sinh \left (9 c_1\right ) x^{15}+8207810320882728960 a^{12} \cosh \left (12 c_1\right ) x^{12}+8207810320882728960 a^{12} \sinh \left (12 c_1\right ) x^{12}-5009649854054400 a^9 \cosh \left (15 c_1\right ) x^9-5009649854054400 a^9 \sinh \left (15 c_1\right ) x^9-978447237120 a^6 \cosh \left (18 c_1\right ) x^6-978447237120 a^6 \sinh \left (18 c_1\right ) x^6+955514880 a^3 \cosh \left (21 c_1\right ) x^3+955514880 a^3 \sinh \left (21 c_1\right ) x^3+186624 \cosh \left (24 c_1\right )+186624 \sinh \left (24 c_1\right )}}}{3888 \sqrt [3]{2} a^2 x^2}+\frac {16 \sqrt [3]{2} \left (4096 a^5 \cosh \left (3 c_1\right ) x^5+4096 a^5 \sinh \left (3 c_1\right ) x^5+5 a^2 \cosh \left (6 c_1\right ) x^2+5 a^2 \sinh \left (6 c_1\right ) x^2\right )}{27 a^2 \sqrt [3]{4529848320 a^6 \cosh \left (6 c_1\right ) x^6+4529848320 a^6 \sinh \left (6 c_1\right ) x^6+1105920 a^3 \cosh \left (9 c_1\right ) x^3+1105920 a^3 \sinh \left (9 c_1\right ) x^3+432 \cosh \left (12 c_1\right )+432 \sinh \left (12 c_1\right )+\sqrt {-3361919107433565782016 a^{15} \cosh \left (9 c_1\right ) x^{15}-3361919107433565782016 a^{15} \sinh \left (9 c_1\right ) x^{15}+8207810320882728960 a^{12} \cosh \left (12 c_1\right ) x^{12}+8207810320882728960 a^{12} \sinh \left (12 c_1\right ) x^{12}-5009649854054400 a^9 \cosh \left (15 c_1\right ) x^9-5009649854054400 a^9 \sinh \left (15 c_1\right ) x^9-978447237120 a^6 \cosh \left (18 c_1\right ) x^6-978447237120 a^6 \sinh \left (18 c_1\right ) x^6+955514880 a^3 \cosh \left (21 c_1\right ) x^3+955514880 a^3 \sinh \left (21 c_1\right ) x^3+186624 \cosh \left (24 c_1\right )+186624 \sinh \left (24 c_1\right )}} x^2}+\frac {\left (1728 a^3 x^3-\cosh \left (3 c_1\right )-\sinh \left (3 c_1\right )\right ){}^2}{419904 a^4 x^4}}-\frac {1}{2} \sqrt {-\frac {128}{9} a^2 x^2-\frac {\frac {\cosh ^3\left (3 c_1\right )}{34012224 a^6 x^6}+\frac {\sinh \left (3 c_1\right ) \cosh ^2\left (3 c_1\right )}{11337408 a^6 x^6}+\frac {\cosh ^2\left (3 c_1\right )}{13122 a^3 x^3}+\frac {\sinh ^2\left (3 c_1\right ) \cosh \left (3 c_1\right )}{11337408 a^6 x^6}+\frac {\sinh \left (3 c_1\right ) \cosh \left (3 c_1\right )}{6561 a^3 x^3}+\frac {512}{243} \cosh \left (3 c_1\right )+\frac {\sinh ^3\left (3 c_1\right )}{34012224 a^6 x^6}+\frac {\sinh ^2\left (3 c_1\right )}{13122 a^3 x^3}+\frac {512}{243} \sinh \left (3 c_1\right )}{4 \sqrt {-\frac {64}{9} a^2 x^2+\frac {\cosh \left (3 c_1\right )}{81 a x}+\frac {\sinh \left (3 c_1\right )}{81 a x}+\frac {\sqrt [3]{4529848320 a^6 \cosh \left (6 c_1\right ) x^6+4529848320 a^6 \sinh \left (6 c_1\right ) x^6+1105920 a^3 \cosh \left (9 c_1\right ) x^3+1105920 a^3 \sinh \left (9 c_1\right ) x^3+432 \cosh \left (12 c_1\right )+432 \sinh \left (12 c_1\right )+\sqrt {-3361919107433565782016 a^{15} \cosh \left (9 c_1\right ) x^{15}-3361919107433565782016 a^{15} \sinh \left (9 c_1\right ) x^{15}+8207810320882728960 a^{12} \cosh \left (12 c_1\right ) x^{12}+8207810320882728960 a^{12} \sinh \left (12 c_1\right ) x^{12}-5009649854054400 a^9 \cosh \left (15 c_1\right ) x^9-5009649854054400 a^9 \sinh \left (15 c_1\right ) x^9-978447237120 a^6 \cosh \left (18 c_1\right ) x^6-978447237120 a^6 \sinh \left (18 c_1\right ) x^6+955514880 a^3 \cosh \left (21 c_1\right ) x^3+955514880 a^3 \sinh \left (21 c_1\right ) x^3+186624 \cosh \left (24 c_1\right )+186624 \sinh \left (24 c_1\right )}}}{3888 \sqrt [3]{2} a^2 x^2}+\frac {16 \sqrt [3]{2} \left (4096 a^5 \cosh \left (3 c_1\right ) x^5+4096 a^5 \sinh \left (3 c_1\right ) x^5+5 a^2 \cosh \left (6 c_1\right ) x^2+5 a^2 \sinh \left (6 c_1\right ) x^2\right )}{27 a^2 \sqrt [3]{4529848320 a^6 \cosh \left (6 c_1\right ) x^6+4529848320 a^6 \sinh \left (6 c_1\right ) x^6+1105920 a^3 \cosh \left (9 c_1\right ) x^3+1105920 a^3 \sinh \left (9 c_1\right ) x^3+432 \cosh \left (12 c_1\right )+432 \sinh \left (12 c_1\right )+\sqrt {-3361919107433565782016 a^{15} \cosh \left (9 c_1\right ) x^{15}-3361919107433565782016 a^{15} \sinh \left (9 c_1\right ) x^{15}+8207810320882728960 a^{12} \cosh \left (12 c_1\right ) x^{12}+8207810320882728960 a^{12} \sinh \left (12 c_1\right ) x^{12}-5009649854054400 a^9 \cosh \left (15 c_1\right ) x^9-5009649854054400 a^9 \sinh \left (15 c_1\right ) x^9-978447237120 a^6 \cosh \left (18 c_1\right ) x^6-978447237120 a^6 \sinh \left (18 c_1\right ) x^6+955514880 a^3 \cosh \left (21 c_1\right ) x^3+955514880 a^3 \sinh \left (21 c_1\right ) x^3+186624 \cosh \left (24 c_1\right )+186624 \sinh \left (24 c_1\right )}} x^2}+\frac {\left (1728 a^3 x^3-\cosh \left (3 c_1\right )-\sinh \left (3 c_1\right )\right ){}^2}{419904 a^4 x^4}}}+\frac {2 \cosh \left (3 c_1\right )}{81 a x}+\frac {2 \sinh \left (3 c_1\right )}{81 a x}-\frac {\sqrt [3]{4529848320 a^6 \cosh \left (6 c_1\right ) x^6+4529848320 a^6 \sinh \left (6 c_1\right ) x^6+1105920 a^3 \cosh \left (9 c_1\right ) x^3+1105920 a^3 \sinh \left (9 c_1\right ) x^3+432 \cosh \left (12 c_1\right )+432 \sinh \left (12 c_1\right )+\sqrt {-3361919107433565782016 a^{15} \cosh \left (9 c_1\right ) x^{15}-3361919107433565782016 a^{15} \sinh \left (9 c_1\right ) x^{15}+8207810320882728960 a^{12} \cosh \left (12 c_1\right ) x^{12}+8207810320882728960 a^{12} \sinh \left (12 c_1\right ) x^{12}-5009649854054400 a^9 \cosh \left (15 c_1\right ) x^9-5009649854054400 a^9 \sinh \left (15 c_1\right ) x^9-978447237120 a^6 \cosh \left (18 c_1\right ) x^6-978447237120 a^6 \sinh \left (18 c_1\right ) x^6+955514880 a^3 \cosh \left (21 c_1\right ) x^3+955514880 a^3 \sinh \left (21 c_1\right ) x^3+186624 \cosh \left (24 c_1\right )+186624 \sinh \left (24 c_1\right )}}}{3888 \sqrt [3]{2} a^2 x^2}-\frac {16 \sqrt [3]{2} \left (4096 a^5 \cosh \left (3 c_1\right ) x^5+4096 a^5 \sinh \left (3 c_1\right ) x^5+5 a^2 \cosh \left (6 c_1\right ) x^2+5 a^2 \sinh \left (6 c_1\right ) x^2\right )}{27 a^2 \sqrt [3]{4529848320 a^6 \cosh \left (6 c_1\right ) x^6+4529848320 a^6 \sinh \left (6 c_1\right ) x^6+1105920 a^3 \cosh \left (9 c_1\right ) x^3+1105920 a^3 \sinh \left (9 c_1\right ) x^3+432 \cosh \left (12 c_1\right )+432 \sinh \left (12 c_1\right )+\sqrt {-3361919107433565782016 a^{15} \cosh \left (9 c_1\right ) x^{15}-3361919107433565782016 a^{15} \sinh \left (9 c_1\right ) x^{15}+8207810320882728960 a^{12} \cosh \left (12 c_1\right ) x^{12}+8207810320882728960 a^{12} \sinh \left (12 c_1\right ) x^{12}-5009649854054400 a^9 \cosh \left (15 c_1\right ) x^9-5009649854054400 a^9 \sinh \left (15 c_1\right ) x^9-978447237120 a^6 \cosh \left (18 c_1\right ) x^6-978447237120 a^6 \sinh \left (18 c_1\right ) x^6+955514880 a^3 \cosh \left (21 c_1\right ) x^3+955514880 a^3 \sinh \left (21 c_1\right ) x^3+186624 \cosh \left (24 c_1\right )+186624 \sinh \left (24 c_1\right )}} x^2}+\frac {\left (1728 a^3 x^3-\cosh \left (3 c_1\right )-\sinh \left (3 c_1\right )\right ){}^2}{209952 a^4 x^4}}+\frac {\cosh \left (3 c_1\right )}{1296 a^2 x^2}+\frac {\sinh \left (3 c_1\right )}{1296 a^2 x^2}}\right \},\left \{y(x)\to -\sqrt {-\frac {4 a x}{3}-\frac {1}{2} \sqrt {-\frac {64}{9} a^2 x^2+\frac {\cosh \left (3 c_1\right )}{81 a x}+\frac {\sinh \left (3 c_1\right )}{81 a x}+\frac {\sqrt [3]{4529848320 a^6 \cosh \left (6 c_1\right ) x^6+4529848320 a^6 \sinh \left (6 c_1\right ) x^6+1105920 a^3 \cosh \left (9 c_1\right ) x^3+1105920 a^3 \sinh \left (9 c_1\right ) x^3+432 \cosh \left (12 c_1\right )+432 \sinh \left (12 c_1\right )+\sqrt {-3361919107433565782016 a^{15} \cosh \left (9 c_1\right ) x^{15}-3361919107433565782016 a^{15} \sinh \left (9 c_1\right ) x^{15}+8207810320882728960 a^{12} \cosh \left (12 c_1\right ) x^{12}+8207810320882728960 a^{12} \sinh \left (12 c_1\right ) x^{12}-5009649854054400 a^9 \cosh \left (15 c_1\right ) x^9-5009649854054400 a^9 \sinh \left (15 c_1\right ) x^9-978447237120 a^6 \cosh \left (18 c_1\right ) x^6-978447237120 a^6 \sinh \left (18 c_1\right ) x^6+955514880 a^3 \cosh \left (21 c_1\right ) x^3+955514880 a^3 \sinh \left (21 c_1\right ) x^3+186624 \cosh \left (24 c_1\right )+186624 \sinh \left (24 c_1\right )}}}{3888 \sqrt [3]{2} a^2 x^2}+\frac {16 \sqrt [3]{2} \left (4096 a^5 \cosh \left (3 c_1\right ) x^5+4096 a^5 \sinh \left (3 c_1\right ) x^5+5 a^2 \cosh \left (6 c_1\right ) x^2+5 a^2 \sinh \left (6 c_1\right ) x^2\right )}{27 a^2 \sqrt [3]{4529848320 a^6 \cosh \left (6 c_1\right ) x^6+4529848320 a^6 \sinh \left (6 c_1\right ) x^6+1105920 a^3 \cosh \left (9 c_1\right ) x^3+1105920 a^3 \sinh \left (9 c_1\right ) x^3+432 \cosh \left (12 c_1\right )+432 \sinh \left (12 c_1\right )+\sqrt {-3361919107433565782016 a^{15} \cosh \left (9 c_1\right ) x^{15}-3361919107433565782016 a^{15} \sinh \left (9 c_1\right ) x^{15}+8207810320882728960 a^{12} \cosh \left (12 c_1\right ) x^{12}+8207810320882728960 a^{12} \sinh \left (12 c_1\right ) x^{12}-5009649854054400 a^9 \cosh \left (15 c_1\right ) x^9-5009649854054400 a^9 \sinh \left (15 c_1\right ) x^9-978447237120 a^6 \cosh \left (18 c_1\right ) x^6-978447237120 a^6 \sinh \left (18 c_1\right ) x^6+955514880 a^3 \cosh \left (21 c_1\right ) x^3+955514880 a^3 \sinh \left (21 c_1\right ) x^3+186624 \cosh \left (24 c_1\right )+186624 \sinh \left (24 c_1\right )}} x^2}+\frac {\left (1728 a^3 x^3-\cosh \left (3 c_1\right )-\sinh \left (3 c_1\right )\right ){}^2}{419904 a^4 x^4}}+\frac {1}{2} \sqrt {-\frac {128}{9} a^2 x^2-\frac {\frac {\cosh ^3\left (3 c_1\right )}{34012224 a^6 x^6}+\frac {\sinh \left (3 c_1\right ) \cosh ^2\left (3 c_1\right )}{11337408 a^6 x^6}+\frac {\cosh ^2\left (3 c_1\right )}{13122 a^3 x^3}+\frac {\sinh ^2\left (3 c_1\right ) \cosh \left (3 c_1\right )}{11337408 a^6 x^6}+\frac {\sinh \left (3 c_1\right ) \cosh \left (3 c_1\right )}{6561 a^3 x^3}+\frac {512}{243} \cosh \left (3 c_1\right )+\frac {\sinh ^3\left (3 c_1\right )}{34012224 a^6 x^6}+\frac {\sinh ^2\left (3 c_1\right )}{13122 a^3 x^3}+\frac {512}{243} \sinh \left (3 c_1\right )}{4 \sqrt {-\frac {64}{9} a^2 x^2+\frac {\cosh \left (3 c_1\right )}{81 a x}+\frac {\sinh \left (3 c_1\right )}{81 a x}+\frac {\sqrt [3]{4529848320 a^6 \cosh \left (6 c_1\right ) x^6+4529848320 a^6 \sinh \left (6 c_1\right ) x^6+1105920 a^3 \cosh \left (9 c_1\right ) x^3+1105920 a^3 \sinh \left (9 c_1\right ) x^3+432 \cosh \left (12 c_1\right )+432 \sinh \left (12 c_1\right )+\sqrt {-3361919107433565782016 a^{15} \cosh \left (9 c_1\right ) x^{15}-3361919107433565782016 a^{15} \sinh \left (9 c_1\right ) x^{15}+8207810320882728960 a^{12} \cosh \left (12 c_1\right ) x^{12}+8207810320882728960 a^{12} \sinh \left (12 c_1\right ) x^{12}-5009649854054400 a^9 \cosh \left (15 c_1\right ) x^9-5009649854054400 a^9 \sinh \left (15 c_1\right ) x^9-978447237120 a^6 \cosh \left (18 c_1\right ) x^6-978447237120 a^6 \sinh \left (18 c_1\right ) x^6+955514880 a^3 \cosh \left (21 c_1\right ) x^3+955514880 a^3 \sinh \left (21 c_1\right ) x^3+186624 \cosh \left (24 c_1\right )+186624 \sinh \left (24 c_1\right )}}}{3888 \sqrt [3]{2} a^2 x^2}+\frac {16 \sqrt [3]{2} \left (4096 a^5 \cosh \left (3 c_1\right ) x^5+4096 a^5 \sinh \left (3 c_1\right ) x^5+5 a^2 \cosh \left (6 c_1\right ) x^2+5 a^2 \sinh \left (6 c_1\right ) x^2\right )}{27 a^2 \sqrt [3]{4529848320 a^6 \cosh \left (6 c_1\right ) x^6+4529848320 a^6 \sinh \left (6 c_1\right ) x^6+1105920 a^3 \cosh \left (9 c_1\right ) x^3+1105920 a^3 \sinh \left (9 c_1\right ) x^3+432 \cosh \left (12 c_1\right )+432 \sinh \left (12 c_1\right )+\sqrt {-3361919107433565782016 a^{15} \cosh \left (9 c_1\right ) x^{15}-3361919107433565782016 a^{15} \sinh \left (9 c_1\right ) x^{15}+8207810320882728960 a^{12} \cosh \left (12 c_1\right ) x^{12}+8207810320882728960 a^{12} \sinh \left (12 c_1\right ) x^{12}-5009649854054400 a^9 \cosh \left (15 c_1\right ) x^9-5009649854054400 a^9 \sinh \left (15 c_1\right ) x^9-978447237120 a^6 \cosh \left (18 c_1\right ) x^6-978447237120 a^6 \sinh \left (18 c_1\right ) x^6+955514880 a^3 \cosh \left (21 c_1\right ) x^3+955514880 a^3 \sinh \left (21 c_1\right ) x^3+186624 \cosh \left (24 c_1\right )+186624 \sinh \left (24 c_1\right )}} x^2}+\frac {\left (1728 a^3 x^3-\cosh \left (3 c_1\right )-\sinh \left (3 c_1\right )\right ){}^2}{419904 a^4 x^4}}}+\frac {2 \cosh \left (3 c_1\right )}{81 a x}+\frac {2 \sinh \left (3 c_1\right )}{81 a x}-\frac {\sqrt [3]{4529848320 a^6 \cosh \left (6 c_1\right ) x^6+4529848320 a^6 \sinh \left (6 c_1\right ) x^6+1105920 a^3 \cosh \left (9 c_1\right ) x^3+1105920 a^3 \sinh \left (9 c_1\right ) x^3+432 \cosh \left (12 c_1\right )+432 \sinh \left (12 c_1\right )+\sqrt {-3361919107433565782016 a^{15} \cosh \left (9 c_1\right ) x^{15}-3361919107433565782016 a^{15} \sinh \left (9 c_1\right ) x^{15}+8207810320882728960 a^{12} \cosh \left (12 c_1\right ) x^{12}+8207810320882728960 a^{12} \sinh \left (12 c_1\right ) x^{12}-5009649854054400 a^9 \cosh \left (15 c_1\right ) x^9-5009649854054400 a^9 \sinh \left (15 c_1\right ) x^9-978447237120 a^6 \cosh \left (18 c_1\right ) x^6-978447237120 a^6 \sinh \left (18 c_1\right ) x^6+955514880 a^3 \cosh \left (21 c_1\right ) x^3+955514880 a^3 \sinh \left (21 c_1\right ) x^3+186624 \cosh \left (24 c_1\right )+186624 \sinh \left (24 c_1\right )}}}{3888 \sqrt [3]{2} a^2 x^2}-\frac {16 \sqrt [3]{2} \left (4096 a^5 \cosh \left (3 c_1\right ) x^5+4096 a^5 \sinh \left (3 c_1\right ) x^5+5 a^2 \cosh \left (6 c_1\right ) x^2+5 a^2 \sinh \left (6 c_1\right ) x^2\right )}{27 a^2 \sqrt [3]{4529848320 a^6 \cosh \left (6 c_1\right ) x^6+4529848320 a^6 \sinh \left (6 c_1\right ) x^6+1105920 a^3 \cosh \left (9 c_1\right ) x^3+1105920 a^3 \sinh \left (9 c_1\right ) x^3+432 \cosh \left (12 c_1\right )+432 \sinh \left (12 c_1\right )+\sqrt {-3361919107433565782016 a^{15} \cosh \left (9 c_1\right ) x^{15}-3361919107433565782016 a^{15} \sinh \left (9 c_1\right ) x^{15}+8207810320882728960 a^{12} \cosh \left (12 c_1\right ) x^{12}+8207810320882728960 a^{12} \sinh \left (12 c_1\right ) x^{12}-5009649854054400 a^9 \cosh \left (15 c_1\right ) x^9-5009649854054400 a^9 \sinh \left (15 c_1\right ) x^9-978447237120 a^6 \cosh \left (18 c_1\right ) x^6-978447237120 a^6 \sinh \left (18 c_1\right ) x^6+955514880 a^3 \cosh \left (21 c_1\right ) x^3+955514880 a^3 \sinh \left (21 c_1\right ) x^3+186624 \cosh \left (24 c_1\right )+186624 \sinh \left (24 c_1\right )}} x^2}+\frac {\left (1728 a^3 x^3-\cosh \left (3 c_1\right )-\sinh \left (3 c_1\right )\right ){}^2}{209952 a^4 x^4}}+\frac {\cosh \left (3 c_1\right )}{1296 a^2 x^2}+\frac {\sinh \left (3 c_1\right )}{1296 a^2 x^2}}\right \},\left \{y(x)\to \sqrt {-\frac {4 a x}{3}-\frac {1}{2} \sqrt {-\frac {64}{9} a^2 x^2+\frac {\cosh \left (3 c_1\right )}{81 a x}+\frac {\sinh \left (3 c_1\right )}{81 a x}+\frac {\sqrt [3]{4529848320 a^6 \cosh \left (6 c_1\right ) x^6+4529848320 a^6 \sinh \left (6 c_1\right ) x^6+1105920 a^3 \cosh \left (9 c_1\right ) x^3+1105920 a^3 \sinh \left (9 c_1\right ) x^3+432 \cosh \left (12 c_1\right )+432 \sinh \left (12 c_1\right )+\sqrt {-3361919107433565782016 a^{15} \cosh \left (9 c_1\right ) x^{15}-3361919107433565782016 a^{15} \sinh \left (9 c_1\right ) x^{15}+8207810320882728960 a^{12} \cosh \left (12 c_1\right ) x^{12}+8207810320882728960 a^{12} \sinh \left (12 c_1\right ) x^{12}-5009649854054400 a^9 \cosh \left (15 c_1\right ) x^9-5009649854054400 a^9 \sinh \left (15 c_1\right ) x^9-978447237120 a^6 \cosh \left (18 c_1\right ) x^6-978447237120 a^6 \sinh \left (18 c_1\right ) x^6+955514880 a^3 \cosh \left (21 c_1\right ) x^3+955514880 a^3 \sinh \left (21 c_1\right ) x^3+186624 \cosh \left (24 c_1\right )+186624 \sinh \left (24 c_1\right )}}}{3888 \sqrt [3]{2} a^2 x^2}+\frac {16 \sqrt [3]{2} \left (4096 a^5 \cosh \left (3 c_1\right ) x^5+4096 a^5 \sinh \left (3 c_1\right ) x^5+5 a^2 \cosh \left (6 c_1\right ) x^2+5 a^2 \sinh \left (6 c_1\right ) x^2\right )}{27 a^2 \sqrt [3]{4529848320 a^6 \cosh \left (6 c_1\right ) x^6+4529848320 a^6 \sinh \left (6 c_1\right ) x^6+1105920 a^3 \cosh \left (9 c_1\right ) x^3+1105920 a^3 \sinh \left (9 c_1\right ) x^3+432 \cosh \left (12 c_1\right )+432 \sinh \left (12 c_1\right )+\sqrt {-3361919107433565782016 a^{15} \cosh \left (9 c_1\right ) x^{15}-3361919107433565782016 a^{15} \sinh \left (9 c_1\right ) x^{15}+8207810320882728960 a^{12} \cosh \left (12 c_1\right ) x^{12}+8207810320882728960 a^{12} \sinh \left (12 c_1\right ) x^{12}-5009649854054400 a^9 \cosh \left (15 c_1\right ) x^9-5009649854054400 a^9 \sinh \left (15 c_1\right ) x^9-978447237120 a^6 \cosh \left (18 c_1\right ) x^6-978447237120 a^6 \sinh \left (18 c_1\right ) x^6+955514880 a^3 \cosh \left (21 c_1\right ) x^3+955514880 a^3 \sinh \left (21 c_1\right ) x^3+186624 \cosh \left (24 c_1\right )+186624 \sinh \left (24 c_1\right )}} x^2}+\frac {\left (1728 a^3 x^3-\cosh \left (3 c_1\right )-\sinh \left (3 c_1\right )\right ){}^2}{419904 a^4 x^4}}+\frac {1}{2} \sqrt {-\frac {128}{9} a^2 x^2-\frac {\frac {\cosh ^3\left (3 c_1\right )}{34012224 a^6 x^6}+\frac {\sinh \left (3 c_1\right ) \cosh ^2\left (3 c_1\right )}{11337408 a^6 x^6}+\frac {\cosh ^2\left (3 c_1\right )}{13122 a^3 x^3}+\frac {\sinh ^2\left (3 c_1\right ) \cosh \left (3 c_1\right )}{11337408 a^6 x^6}+\frac {\sinh \left (3 c_1\right ) \cosh \left (3 c_1\right )}{6561 a^3 x^3}+\frac {512}{243} \cosh \left (3 c_1\right )+\frac {\sinh ^3\left (3 c_1\right )}{34012224 a^6 x^6}+\frac {\sinh ^2\left (3 c_1\right )}{13122 a^3 x^3}+\frac {512}{243} \sinh \left (3 c_1\right )}{4 \sqrt {-\frac {64}{9} a^2 x^2+\frac {\cosh \left (3 c_1\right )}{81 a x}+\frac {\sinh \left (3 c_1\right )}{81 a x}+\frac {\sqrt [3]{4529848320 a^6 \cosh \left (6 c_1\right ) x^6+4529848320 a^6 \sinh \left (6 c_1\right ) x^6+1105920 a^3 \cosh \left (9 c_1\right ) x^3+1105920 a^3 \sinh \left (9 c_1\right ) x^3+432 \cosh \left (12 c_1\right )+432 \sinh \left (12 c_1\right )+\sqrt {-3361919107433565782016 a^{15} \cosh \left (9 c_1\right ) x^{15}-3361919107433565782016 a^{15} \sinh \left (9 c_1\right ) x^{15}+8207810320882728960 a^{12} \cosh \left (12 c_1\right ) x^{12}+8207810320882728960 a^{12} \sinh \left (12 c_1\right ) x^{12}-5009649854054400 a^9 \cosh \left (15 c_1\right ) x^9-5009649854054400 a^9 \sinh \left (15 c_1\right ) x^9-978447237120 a^6 \cosh \left (18 c_1\right ) x^6-978447237120 a^6 \sinh \left (18 c_1\right ) x^6+955514880 a^3 \cosh \left (21 c_1\right ) x^3+955514880 a^3 \sinh \left (21 c_1\right ) x^3+186624 \cosh \left (24 c_1\right )+186624 \sinh \left (24 c_1\right )}}}{3888 \sqrt [3]{2} a^2 x^2}+\frac {16 \sqrt [3]{2} \left (4096 a^5 \cosh \left (3 c_1\right ) x^5+4096 a^5 \sinh \left (3 c_1\right ) x^5+5 a^2 \cosh \left (6 c_1\right ) x^2+5 a^2 \sinh \left (6 c_1\right ) x^2\right )}{27 a^2 \sqrt [3]{4529848320 a^6 \cosh \left (6 c_1\right ) x^6+4529848320 a^6 \sinh \left (6 c_1\right ) x^6+1105920 a^3 \cosh \left (9 c_1\right ) x^3+1105920 a^3 \sinh \left (9 c_1\right ) x^3+432 \cosh \left (12 c_1\right )+432 \sinh \left (12 c_1\right )+\sqrt {-3361919107433565782016 a^{15} \cosh \left (9 c_1\right ) x^{15}-3361919107433565782016 a^{15} \sinh \left (9 c_1\right ) x^{15}+8207810320882728960 a^{12} \cosh \left (12 c_1\right ) x^{12}+8207810320882728960 a^{12} \sinh \left (12 c_1\right ) x^{12}-5009649854054400 a^9 \cosh \left (15 c_1\right ) x^9-5009649854054400 a^9 \sinh \left (15 c_1\right ) x^9-978447237120 a^6 \cosh \left (18 c_1\right ) x^6-978447237120 a^6 \sinh \left (18 c_1\right ) x^6+955514880 a^3 \cosh \left (21 c_1\right ) x^3+955514880 a^3 \sinh \left (21 c_1\right ) x^3+186624 \cosh \left (24 c_1\right )+186624 \sinh \left (24 c_1\right )}} x^2}+\frac {\left (1728 a^3 x^3-\cosh \left (3 c_1\right )-\sinh \left (3 c_1\right )\right ){}^2}{419904 a^4 x^4}}}+\frac {2 \cosh \left (3 c_1\right )}{81 a x}+\frac {2 \sinh \left (3 c_1\right )}{81 a x}-\frac {\sqrt [3]{4529848320 a^6 \cosh \left (6 c_1\right ) x^6+4529848320 a^6 \sinh \left (6 c_1\right ) x^6+1105920 a^3 \cosh \left (9 c_1\right ) x^3+1105920 a^3 \sinh \left (9 c_1\right ) x^3+432 \cosh \left (12 c_1\right )+432 \sinh \left (12 c_1\right )+\sqrt {-3361919107433565782016 a^{15} \cosh \left (9 c_1\right ) x^{15}-3361919107433565782016 a^{15} \sinh \left (9 c_1\right ) x^{15}+8207810320882728960 a^{12} \cosh \left (12 c_1\right ) x^{12}+8207810320882728960 a^{12} \sinh \left (12 c_1\right ) x^{12}-5009649854054400 a^9 \cosh \left (15 c_1\right ) x^9-5009649854054400 a^9 \sinh \left (15 c_1\right ) x^9-978447237120 a^6 \cosh \left (18 c_1\right ) x^6-978447237120 a^6 \sinh \left (18 c_1\right ) x^6+955514880 a^3 \cosh \left (21 c_1\right ) x^3+955514880 a^3 \sinh \left (21 c_1\right ) x^3+186624 \cosh \left (24 c_1\right )+186624 \sinh \left (24 c_1\right )}}}{3888 \sqrt [3]{2} a^2 x^2}-\frac {16 \sqrt [3]{2} \left (4096 a^5 \cosh \left (3 c_1\right ) x^5+4096 a^5 \sinh \left (3 c_1\right ) x^5+5 a^2 \cosh \left (6 c_1\right ) x^2+5 a^2 \sinh \left (6 c_1\right ) x^2\right )}{27 a^2 \sqrt [3]{4529848320 a^6 \cosh \left (6 c_1\right ) x^6+4529848320 a^6 \sinh \left (6 c_1\right ) x^6+1105920 a^3 \cosh \left (9 c_1\right ) x^3+1105920 a^3 \sinh \left (9 c_1\right ) x^3+432 \cosh \left (12 c_1\right )+432 \sinh \left (12 c_1\right )+\sqrt {-3361919107433565782016 a^{15} \cosh \left (9 c_1\right ) x^{15}-3361919107433565782016 a^{15} \sinh \left (9 c_1\right ) x^{15}+8207810320882728960 a^{12} \cosh \left (12 c_1\right ) x^{12}+8207810320882728960 a^{12} \sinh \left (12 c_1\right ) x^{12}-5009649854054400 a^9 \cosh \left (15 c_1\right ) x^9-5009649854054400 a^9 \sinh \left (15 c_1\right ) x^9-978447237120 a^6 \cosh \left (18 c_1\right ) x^6-978447237120 a^6 \sinh \left (18 c_1\right ) x^6+955514880 a^3 \cosh \left (21 c_1\right ) x^3+955514880 a^3 \sinh \left (21 c_1\right ) x^3+186624 \cosh \left (24 c_1\right )+186624 \sinh \left (24 c_1\right )}} x^2}+\frac {\left (1728 a^3 x^3-\cosh \left (3 c_1\right )-\sinh \left (3 c_1\right )\right ){}^2}{209952 a^4 x^4}}+\frac {\cosh \left (3 c_1\right )}{1296 a^2 x^2}+\frac {\sinh \left (3 c_1\right )}{1296 a^2 x^2}}\right \},\left \{y(x)\to -\sqrt {-\frac {4 a x}{3}+\frac {1}{2} \sqrt {-\frac {64}{9} a^2 x^2+\frac {\cosh \left (3 c_1\right )}{81 a x}+\frac {\sinh \left (3 c_1\right )}{81 a x}+\frac {\sqrt [3]{4529848320 a^6 \cosh \left (6 c_1\right ) x^6+4529848320 a^6 \sinh \left (6 c_1\right ) x^6+1105920 a^3 \cosh \left (9 c_1\right ) x^3+1105920 a^3 \sinh \left (9 c_1\right ) x^3+432 \cosh \left (12 c_1\right )+432 \sinh \left (12 c_1\right )+\sqrt {-3361919107433565782016 a^{15} \cosh \left (9 c_1\right ) x^{15}-3361919107433565782016 a^{15} \sinh \left (9 c_1\right ) x^{15}+8207810320882728960 a^{12} \cosh \left (12 c_1\right ) x^{12}+8207810320882728960 a^{12} \sinh \left (12 c_1\right ) x^{12}-5009649854054400 a^9 \cosh \left (15 c_1\right ) x^9-5009649854054400 a^9 \sinh \left (15 c_1\right ) x^9-978447237120 a^6 \cosh \left (18 c_1\right ) x^6-978447237120 a^6 \sinh \left (18 c_1\right ) x^6+955514880 a^3 \cosh \left (21 c_1\right ) x^3+955514880 a^3 \sinh \left (21 c_1\right ) x^3+186624 \cosh \left (24 c_1\right )+186624 \sinh \left (24 c_1\right )}}}{3888 \sqrt [3]{2} a^2 x^2}+\frac {16 \sqrt [3]{2} \left (4096 a^5 \cosh \left (3 c_1\right ) x^5+4096 a^5 \sinh \left (3 c_1\right ) x^5+5 a^2 \cosh \left (6 c_1\right ) x^2+5 a^2 \sinh \left (6 c_1\right ) x^2\right )}{27 a^2 \sqrt [3]{4529848320 a^6 \cosh \left (6 c_1\right ) x^6+4529848320 a^6 \sinh \left (6 c_1\right ) x^6+1105920 a^3 \cosh \left (9 c_1\right ) x^3+1105920 a^3 \sinh \left (9 c_1\right ) x^3+432 \cosh \left (12 c_1\right )+432 \sinh \left (12 c_1\right )+\sqrt {-3361919107433565782016 a^{15} \cosh \left (9 c_1\right ) x^{15}-3361919107433565782016 a^{15} \sinh \left (9 c_1\right ) x^{15}+8207810320882728960 a^{12} \cosh \left (12 c_1\right ) x^{12}+8207810320882728960 a^{12} \sinh \left (12 c_1\right ) x^{12}-5009649854054400 a^9 \cosh \left (15 c_1\right ) x^9-5009649854054400 a^9 \sinh \left (15 c_1\right ) x^9-978447237120 a^6 \cosh \left (18 c_1\right ) x^6-978447237120 a^6 \sinh \left (18 c_1\right ) x^6+955514880 a^3 \cosh \left (21 c_1\right ) x^3+955514880 a^3 \sinh \left (21 c_1\right ) x^3+186624 \cosh \left (24 c_1\right )+186624 \sinh \left (24 c_1\right )}} x^2}+\frac {\left (1728 a^3 x^3-\cosh \left (3 c_1\right )-\sinh \left (3 c_1\right )\right ){}^2}{419904 a^4 x^4}}-\frac {1}{2} \sqrt {-\frac {128}{9} a^2 x^2+\frac {\frac {\cosh ^3\left (3 c_1\right )}{34012224 a^6 x^6}+\frac {\sinh \left (3 c_1\right ) \cosh ^2\left (3 c_1\right )}{11337408 a^6 x^6}+\frac {\cosh ^2\left (3 c_1\right )}{13122 a^3 x^3}+\frac {\sinh ^2\left (3 c_1\right ) \cosh \left (3 c_1\right )}{11337408 a^6 x^6}+\frac {\sinh \left (3 c_1\right ) \cosh \left (3 c_1\right )}{6561 a^3 x^3}+\frac {512}{243} \cosh \left (3 c_1\right )+\frac {\sinh ^3\left (3 c_1\right )}{34012224 a^6 x^6}+\frac {\sinh ^2\left (3 c_1\right )}{13122 a^3 x^3}+\frac {512}{243} \sinh \left (3 c_1\right )}{4 \sqrt {-\frac {64}{9} a^2 x^2+\frac {\cosh \left (3 c_1\right )}{81 a x}+\frac {\sinh \left (3 c_1\right )}{81 a x}+\frac {\sqrt [3]{4529848320 a^6 \cosh \left (6 c_1\right ) x^6+4529848320 a^6 \sinh \left (6 c_1\right ) x^6+1105920 a^3 \cosh \left (9 c_1\right ) x^3+1105920 a^3 \sinh \left (9 c_1\right ) x^3+432 \cosh \left (12 c_1\right )+432 \sinh \left (12 c_1\right )+\sqrt {-3361919107433565782016 a^{15} \cosh \left (9 c_1\right ) x^{15}-3361919107433565782016 a^{15} \sinh \left (9 c_1\right ) x^{15}+8207810320882728960 a^{12} \cosh \left (12 c_1\right ) x^{12}+8207810320882728960 a^{12} \sinh \left (12 c_1\right ) x^{12}-5009649854054400 a^9 \cosh \left (15 c_1\right ) x^9-5009649854054400 a^9 \sinh \left (15 c_1\right ) x^9-978447237120 a^6 \cosh \left (18 c_1\right ) x^6-978447237120 a^6 \sinh \left (18 c_1\right ) x^6+955514880 a^3 \cosh \left (21 c_1\right ) x^3+955514880 a^3 \sinh \left (21 c_1\right ) x^3+186624 \cosh \left (24 c_1\right )+186624 \sinh \left (24 c_1\right )}}}{3888 \sqrt [3]{2} a^2 x^2}+\frac {16 \sqrt [3]{2} \left (4096 a^5 \cosh \left (3 c_1\right ) x^5+4096 a^5 \sinh \left (3 c_1\right ) x^5+5 a^2 \cosh \left (6 c_1\right ) x^2+5 a^2 \sinh \left (6 c_1\right ) x^2\right )}{27 a^2 \sqrt [3]{4529848320 a^6 \cosh \left (6 c_1\right ) x^6+4529848320 a^6 \sinh \left (6 c_1\right ) x^6+1105920 a^3 \cosh \left (9 c_1\right ) x^3+1105920 a^3 \sinh \left (9 c_1\right ) x^3+432 \cosh \left (12 c_1\right )+432 \sinh \left (12 c_1\right )+\sqrt {-3361919107433565782016 a^{15} \cosh \left (9 c_1\right ) x^{15}-3361919107433565782016 a^{15} \sinh \left (9 c_1\right ) x^{15}+8207810320882728960 a^{12} \cosh \left (12 c_1\right ) x^{12}+8207810320882728960 a^{12} \sinh \left (12 c_1\right ) x^{12}-5009649854054400 a^9 \cosh \left (15 c_1\right ) x^9-5009649854054400 a^9 \sinh \left (15 c_1\right ) x^9-978447237120 a^6 \cosh \left (18 c_1\right ) x^6-978447237120 a^6 \sinh \left (18 c_1\right ) x^6+955514880 a^3 \cosh \left (21 c_1\right ) x^3+955514880 a^3 \sinh \left (21 c_1\right ) x^3+186624 \cosh \left (24 c_1\right )+186624 \sinh \left (24 c_1\right )}} x^2}+\frac {\left (1728 a^3 x^3-\cosh \left (3 c_1\right )-\sinh \left (3 c_1\right )\right ){}^2}{419904 a^4 x^4}}}+\frac {2 \cosh \left (3 c_1\right )}{81 a x}+\frac {2 \sinh \left (3 c_1\right )}{81 a x}-\frac {\sqrt [3]{4529848320 a^6 \cosh \left (6 c_1\right ) x^6+4529848320 a^6 \sinh \left (6 c_1\right ) x^6+1105920 a^3 \cosh \left (9 c_1\right ) x^3+1105920 a^3 \sinh \left (9 c_1\right ) x^3+432 \cosh \left (12 c_1\right )+432 \sinh \left (12 c_1\right )+\sqrt {-3361919107433565782016 a^{15} \cosh \left (9 c_1\right ) x^{15}-3361919107433565782016 a^{15} \sinh \left (9 c_1\right ) x^{15}+8207810320882728960 a^{12} \cosh \left (12 c_1\right ) x^{12}+8207810320882728960 a^{12} \sinh \left (12 c_1\right ) x^{12}-5009649854054400 a^9 \cosh \left (15 c_1\right ) x^9-5009649854054400 a^9 \sinh \left (15 c_1\right ) x^9-978447237120 a^6 \cosh \left (18 c_1\right ) x^6-978447237120 a^6 \sinh \left (18 c_1\right ) x^6+955514880 a^3 \cosh \left (21 c_1\right ) x^3+955514880 a^3 \sinh \left (21 c_1\right ) x^3+186624 \cosh \left (24 c_1\right )+186624 \sinh \left (24 c_1\right )}}}{3888 \sqrt [3]{2} a^2 x^2}-\frac {16 \sqrt [3]{2} \left (4096 a^5 \cosh \left (3 c_1\right ) x^5+4096 a^5 \sinh \left (3 c_1\right ) x^5+5 a^2 \cosh \left (6 c_1\right ) x^2+5 a^2 \sinh \left (6 c_1\right ) x^2\right )}{27 a^2 \sqrt [3]{4529848320 a^6 \cosh \left (6 c_1\right ) x^6+4529848320 a^6 \sinh \left (6 c_1\right ) x^6+1105920 a^3 \cosh \left (9 c_1\right ) x^3+1105920 a^3 \sinh \left (9 c_1\right ) x^3+432 \cosh \left (12 c_1\right )+432 \sinh \left (12 c_1\right )+\sqrt {-3361919107433565782016 a^{15} \cosh \left (9 c_1\right ) x^{15}-3361919107433565782016 a^{15} \sinh \left (9 c_1\right ) x^{15}+8207810320882728960 a^{12} \cosh \left (12 c_1\right ) x^{12}+8207810320882728960 a^{12} \sinh \left (12 c_1\right ) x^{12}-5009649854054400 a^9 \cosh \left (15 c_1\right ) x^9-5009649854054400 a^9 \sinh \left (15 c_1\right ) x^9-978447237120 a^6 \cosh \left (18 c_1\right ) x^6-978447237120 a^6 \sinh \left (18 c_1\right ) x^6+955514880 a^3 \cosh \left (21 c_1\right ) x^3+955514880 a^3 \sinh \left (21 c_1\right ) x^3+186624 \cosh \left (24 c_1\right )+186624 \sinh \left (24 c_1\right )}} x^2}+\frac {\left (1728 a^3 x^3-\cosh \left (3 c_1\right )-\sinh \left (3 c_1\right )\right ){}^2}{209952 a^4 x^4}}+\frac {\cosh \left (3 c_1\right )}{1296 a^2 x^2}+\frac {\sinh \left (3 c_1\right )}{1296 a^2 x^2}}\right \},\left \{y(x)\to \sqrt {-\frac {4 a x}{3}+\frac {1}{2} \sqrt {-\frac {64}{9} a^2 x^2+\frac {\cosh \left (3 c_1\right )}{81 a x}+\frac {\sinh \left (3 c_1\right )}{81 a x}+\frac {\sqrt [3]{4529848320 a^6 \cosh \left (6 c_1\right ) x^6+4529848320 a^6 \sinh \left (6 c_1\right ) x^6+1105920 a^3 \cosh \left (9 c_1\right ) x^3+1105920 a^3 \sinh \left (9 c_1\right ) x^3+432 \cosh \left (12 c_1\right )+432 \sinh \left (12 c_1\right )+\sqrt {-3361919107433565782016 a^{15} \cosh \left (9 c_1\right ) x^{15}-3361919107433565782016 a^{15} \sinh \left (9 c_1\right ) x^{15}+8207810320882728960 a^{12} \cosh \left (12 c_1\right ) x^{12}+8207810320882728960 a^{12} \sinh \left (12 c_1\right ) x^{12}-5009649854054400 a^9 \cosh \left (15 c_1\right ) x^9-5009649854054400 a^9 \sinh \left (15 c_1\right ) x^9-978447237120 a^6 \cosh \left (18 c_1\right ) x^6-978447237120 a^6 \sinh \left (18 c_1\right ) x^6+955514880 a^3 \cosh \left (21 c_1\right ) x^3+955514880 a^3 \sinh \left (21 c_1\right ) x^3+186624 \cosh \left (24 c_1\right )+186624 \sinh \left (24 c_1\right )}}}{3888 \sqrt [3]{2} a^2 x^2}+\frac {16 \sqrt [3]{2} \left (4096 a^5 \cosh \left (3 c_1\right ) x^5+4096 a^5 \sinh \left (3 c_1\right ) x^5+5 a^2 \cosh \left (6 c_1\right ) x^2+5 a^2 \sinh \left (6 c_1\right ) x^2\right )}{27 a^2 \sqrt [3]{4529848320 a^6 \cosh \left (6 c_1\right ) x^6+4529848320 a^6 \sinh \left (6 c_1\right ) x^6+1105920 a^3 \cosh \left (9 c_1\right ) x^3+1105920 a^3 \sinh \left (9 c_1\right ) x^3+432 \cosh \left (12 c_1\right )+432 \sinh \left (12 c_1\right )+\sqrt {-3361919107433565782016 a^{15} \cosh \left (9 c_1\right ) x^{15}-3361919107433565782016 a^{15} \sinh \left (9 c_1\right ) x^{15}+8207810320882728960 a^{12} \cosh \left (12 c_1\right ) x^{12}+8207810320882728960 a^{12} \sinh \left (12 c_1\right ) x^{12}-5009649854054400 a^9 \cosh \left (15 c_1\right ) x^9-5009649854054400 a^9 \sinh \left (15 c_1\right ) x^9-978447237120 a^6 \cosh \left (18 c_1\right ) x^6-978447237120 a^6 \sinh \left (18 c_1\right ) x^6+955514880 a^3 \cosh \left (21 c_1\right ) x^3+955514880 a^3 \sinh \left (21 c_1\right ) x^3+186624 \cosh \left (24 c_1\right )+186624 \sinh \left (24 c_1\right )}} x^2}+\frac {\left (1728 a^3 x^3-\cosh \left (3 c_1\right )-\sinh \left (3 c_1\right )\right ){}^2}{419904 a^4 x^4}}-\frac {1}{2} \sqrt {-\frac {128}{9} a^2 x^2+\frac {\frac {\cosh ^3\left (3 c_1\right )}{34012224 a^6 x^6}+\frac {\sinh \left (3 c_1\right ) \cosh ^2\left (3 c_1\right )}{11337408 a^6 x^6}+\frac {\cosh ^2\left (3 c_1\right )}{13122 a^3 x^3}+\frac {\sinh ^2\left (3 c_1\right ) \cosh \left (3 c_1\right )}{11337408 a^6 x^6}+\frac {\sinh \left (3 c_1\right ) \cosh \left (3 c_1\right )}{6561 a^3 x^3}+\frac {512}{243} \cosh \left (3 c_1\right )+\frac {\sinh ^3\left (3 c_1\right )}{34012224 a^6 x^6}+\frac {\sinh ^2\left (3 c_1\right )}{13122 a^3 x^3}+\frac {512}{243} \sinh \left (3 c_1\right )}{4 \sqrt {-\frac {64}{9} a^2 x^2+\frac {\cosh \left (3 c_1\right )}{81 a x}+\frac {\sinh \left (3 c_1\right )}{81 a x}+\frac {\sqrt [3]{4529848320 a^6 \cosh \left (6 c_1\right ) x^6+4529848320 a^6 \sinh \left (6 c_1\right ) x^6+1105920 a^3 \cosh \left (9 c_1\right ) x^3+1105920 a^3 \sinh \left (9 c_1\right ) x^3+432 \cosh \left (12 c_1\right )+432 \sinh \left (12 c_1\right )+\sqrt {-3361919107433565782016 a^{15} \cosh \left (9 c_1\right ) x^{15}-3361919107433565782016 a^{15} \sinh \left (9 c_1\right ) x^{15}+8207810320882728960 a^{12} \cosh \left (12 c_1\right ) x^{12}+8207810320882728960 a^{12} \sinh \left (12 c_1\right ) x^{12}-5009649854054400 a^9 \cosh \left (15 c_1\right ) x^9-5009649854054400 a^9 \sinh \left (15 c_1\right ) x^9-978447237120 a^6 \cosh \left (18 c_1\right ) x^6-978447237120 a^6 \sinh \left (18 c_1\right ) x^6+955514880 a^3 \cosh \left (21 c_1\right ) x^3+955514880 a^3 \sinh \left (21 c_1\right ) x^3+186624 \cosh \left (24 c_1\right )+186624 \sinh \left (24 c_1\right )}}}{3888 \sqrt [3]{2} a^2 x^2}+\frac {16 \sqrt [3]{2} \left (4096 a^5 \cosh \left (3 c_1\right ) x^5+4096 a^5 \sinh \left (3 c_1\right ) x^5+5 a^2 \cosh \left (6 c_1\right ) x^2+5 a^2 \sinh \left (6 c_1\right ) x^2\right )}{27 a^2 \sqrt [3]{4529848320 a^6 \cosh \left (6 c_1\right ) x^6+4529848320 a^6 \sinh \left (6 c_1\right ) x^6+1105920 a^3 \cosh \left (9 c_1\right ) x^3+1105920 a^3 \sinh \left (9 c_1\right ) x^3+432 \cosh \left (12 c_1\right )+432 \sinh \left (12 c_1\right )+\sqrt {-3361919107433565782016 a^{15} \cosh \left (9 c_1\right ) x^{15}-3361919107433565782016 a^{15} \sinh \left (9 c_1\right ) x^{15}+8207810320882728960 a^{12} \cosh \left (12 c_1\right ) x^{12}+8207810320882728960 a^{12} \sinh \left (12 c_1\right ) x^{12}-5009649854054400 a^9 \cosh \left (15 c_1\right ) x^9-5009649854054400 a^9 \sinh \left (15 c_1\right ) x^9-978447237120 a^6 \cosh \left (18 c_1\right ) x^6-978447237120 a^6 \sinh \left (18 c_1\right ) x^6+955514880 a^3 \cosh \left (21 c_1\right ) x^3+955514880 a^3 \sinh \left (21 c_1\right ) x^3+186624 \cosh \left (24 c_1\right )+186624 \sinh \left (24 c_1\right )}} x^2}+\frac {\left (1728 a^3 x^3-\cosh \left (3 c_1\right )-\sinh \left (3 c_1\right )\right ){}^2}{419904 a^4 x^4}}}+\frac {2 \cosh \left (3 c_1\right )}{81 a x}+\frac {2 \sinh \left (3 c_1\right )}{81 a x}-\frac {\sqrt [3]{4529848320 a^6 \cosh \left (6 c_1\right ) x^6+4529848320 a^6 \sinh \left (6 c_1\right ) x^6+1105920 a^3 \cosh \left (9 c_1\right ) x^3+1105920 a^3 \sinh \left (9 c_1\right ) x^3+432 \cosh \left (12 c_1\right )+432 \sinh \left (12 c_1\right )+\sqrt {-3361919107433565782016 a^{15} \cosh \left (9 c_1\right ) x^{15}-3361919107433565782016 a^{15} \sinh \left (9 c_1\right ) x^{15}+8207810320882728960 a^{12} \cosh \left (12 c_1\right ) x^{12}+8207810320882728960 a^{12} \sinh \left (12 c_1\right ) x^{12}-5009649854054400 a^9 \cosh \left (15 c_1\right ) x^9-5009649854054400 a^9 \sinh \left (15 c_1\right ) x^9-978447237120 a^6 \cosh \left (18 c_1\right ) x^6-978447237120 a^6 \sinh \left (18 c_1\right ) x^6+955514880 a^3 \cosh \left (21 c_1\right ) x^3+955514880 a^3 \sinh \left (21 c_1\right ) x^3+186624 \cosh \left (24 c_1\right )+186624 \sinh \left (24 c_1\right )}}}{3888 \sqrt [3]{2} a^2 x^2}-\frac {16 \sqrt [3]{2} \left (4096 a^5 \cosh \left (3 c_1\right ) x^5+4096 a^5 \sinh \left (3 c_1\right ) x^5+5 a^2 \cosh \left (6 c_1\right ) x^2+5 a^2 \sinh \left (6 c_1\right ) x^2\right )}{27 a^2 \sqrt [3]{4529848320 a^6 \cosh \left (6 c_1\right ) x^6+4529848320 a^6 \sinh \left (6 c_1\right ) x^6+1105920 a^3 \cosh \left (9 c_1\right ) x^3+1105920 a^3 \sinh \left (9 c_1\right ) x^3+432 \cosh \left (12 c_1\right )+432 \sinh \left (12 c_1\right )+\sqrt {-3361919107433565782016 a^{15} \cosh \left (9 c_1\right ) x^{15}-3361919107433565782016 a^{15} \sinh \left (9 c_1\right ) x^{15}+8207810320882728960 a^{12} \cosh \left (12 c_1\right ) x^{12}+8207810320882728960 a^{12} \sinh \left (12 c_1\right ) x^{12}-5009649854054400 a^9 \cosh \left (15 c_1\right ) x^9-5009649854054400 a^9 \sinh \left (15 c_1\right ) x^9-978447237120 a^6 \cosh \left (18 c_1\right ) x^6-978447237120 a^6 \sinh \left (18 c_1\right ) x^6+955514880 a^3 \cosh \left (21 c_1\right ) x^3+955514880 a^3 \sinh \left (21 c_1\right ) x^3+186624 \cosh \left (24 c_1\right )+186624 \sinh \left (24 c_1\right )}} x^2}+\frac {\left (1728 a^3 x^3-\cosh \left (3 c_1\right )-\sinh \left (3 c_1\right )\right ){}^2}{209952 a^4 x^4}}+\frac {\cosh \left (3 c_1\right )}{1296 a^2 x^2}+\frac {\sinh \left (3 c_1\right )}{1296 a^2 x^2}}\right \},\left \{y(x)\to -\sqrt {-\frac {4 a x}{3}+\frac {1}{2} \sqrt {-\frac {64}{9} a^2 x^2+\frac {\cosh \left (3 c_1\right )}{81 a x}+\frac {\sinh \left (3 c_1\right )}{81 a x}+\frac {\sqrt [3]{4529848320 a^6 \cosh \left (6 c_1\right ) x^6+4529848320 a^6 \sinh \left (6 c_1\right ) x^6+1105920 a^3 \cosh \left (9 c_1\right ) x^3+1105920 a^3 \sinh \left (9 c_1\right ) x^3+432 \cosh \left (12 c_1\right )+432 \sinh \left (12 c_1\right )+\sqrt {-3361919107433565782016 a^{15} \cosh \left (9 c_1\right ) x^{15}-3361919107433565782016 a^{15} \sinh \left (9 c_1\right ) x^{15}+8207810320882728960 a^{12} \cosh \left (12 c_1\right ) x^{12}+8207810320882728960 a^{12} \sinh \left (12 c_1\right ) x^{12}-5009649854054400 a^9 \cosh \left (15 c_1\right ) x^9-5009649854054400 a^9 \sinh \left (15 c_1\right ) x^9-978447237120 a^6 \cosh \left (18 c_1\right ) x^6-978447237120 a^6 \sinh \left (18 c_1\right ) x^6+955514880 a^3 \cosh \left (21 c_1\right ) x^3+955514880 a^3 \sinh \left (21 c_1\right ) x^3+186624 \cosh \left (24 c_1\right )+186624 \sinh \left (24 c_1\right )}}}{3888 \sqrt [3]{2} a^2 x^2}+\frac {16 \sqrt [3]{2} \left (4096 a^5 \cosh \left (3 c_1\right ) x^5+4096 a^5 \sinh \left (3 c_1\right ) x^5+5 a^2 \cosh \left (6 c_1\right ) x^2+5 a^2 \sinh \left (6 c_1\right ) x^2\right )}{27 a^2 \sqrt [3]{4529848320 a^6 \cosh \left (6 c_1\right ) x^6+4529848320 a^6 \sinh \left (6 c_1\right ) x^6+1105920 a^3 \cosh \left (9 c_1\right ) x^3+1105920 a^3 \sinh \left (9 c_1\right ) x^3+432 \cosh \left (12 c_1\right )+432 \sinh \left (12 c_1\right )+\sqrt {-3361919107433565782016 a^{15} \cosh \left (9 c_1\right ) x^{15}-3361919107433565782016 a^{15} \sinh \left (9 c_1\right ) x^{15}+8207810320882728960 a^{12} \cosh \left (12 c_1\right ) x^{12}+8207810320882728960 a^{12} \sinh \left (12 c_1\right ) x^{12}-5009649854054400 a^9 \cosh \left (15 c_1\right ) x^9-5009649854054400 a^9 \sinh \left (15 c_1\right ) x^9-978447237120 a^6 \cosh \left (18 c_1\right ) x^6-978447237120 a^6 \sinh \left (18 c_1\right ) x^6+955514880 a^3 \cosh \left (21 c_1\right ) x^3+955514880 a^3 \sinh \left (21 c_1\right ) x^3+186624 \cosh \left (24 c_1\right )+186624 \sinh \left (24 c_1\right )}} x^2}+\frac {\left (1728 a^3 x^3-\cosh \left (3 c_1\right )-\sinh \left (3 c_1\right )\right ){}^2}{419904 a^4 x^4}}+\frac {1}{2} \sqrt {-\frac {128}{9} a^2 x^2+\frac {\frac {\cosh ^3\left (3 c_1\right )}{34012224 a^6 x^6}+\frac {\sinh \left (3 c_1\right ) \cosh ^2\left (3 c_1\right )}{11337408 a^6 x^6}+\frac {\cosh ^2\left (3 c_1\right )}{13122 a^3 x^3}+\frac {\sinh ^2\left (3 c_1\right ) \cosh \left (3 c_1\right )}{11337408 a^6 x^6}+\frac {\sinh \left (3 c_1\right ) \cosh \left (3 c_1\right )}{6561 a^3 x^3}+\frac {512}{243} \cosh \left (3 c_1\right )+\frac {\sinh ^3\left (3 c_1\right )}{34012224 a^6 x^6}+\frac {\sinh ^2\left (3 c_1\right )}{13122 a^3 x^3}+\frac {512}{243} \sinh \left (3 c_1\right )}{4 \sqrt {-\frac {64}{9} a^2 x^2+\frac {\cosh \left (3 c_1\right )}{81 a x}+\frac {\sinh \left (3 c_1\right )}{81 a x}+\frac {\sqrt [3]{4529848320 a^6 \cosh \left (6 c_1\right ) x^6+4529848320 a^6 \sinh \left (6 c_1\right ) x^6+1105920 a^3 \cosh \left (9 c_1\right ) x^3+1105920 a^3 \sinh \left (9 c_1\right ) x^3+432 \cosh \left (12 c_1\right )+432 \sinh \left (12 c_1\right )+\sqrt {-3361919107433565782016 a^{15} \cosh \left (9 c_1\right ) x^{15}-3361919107433565782016 a^{15} \sinh \left (9 c_1\right ) x^{15}+8207810320882728960 a^{12} \cosh \left (12 c_1\right ) x^{12}+8207810320882728960 a^{12} \sinh \left (12 c_1\right ) x^{12}-5009649854054400 a^9 \cosh \left (15 c_1\right ) x^9-5009649854054400 a^9 \sinh \left (15 c_1\right ) x^9-978447237120 a^6 \cosh \left (18 c_1\right ) x^6-978447237120 a^6 \sinh \left (18 c_1\right ) x^6+955514880 a^3 \cosh \left (21 c_1\right ) x^3+955514880 a^3 \sinh \left (21 c_1\right ) x^3+186624 \cosh \left (24 c_1\right )+186624 \sinh \left (24 c_1\right )}}}{3888 \sqrt [3]{2} a^2 x^2}+\frac {16 \sqrt [3]{2} \left (4096 a^5 \cosh \left (3 c_1\right ) x^5+4096 a^5 \sinh \left (3 c_1\right ) x^5+5 a^2 \cosh \left (6 c_1\right ) x^2+5 a^2 \sinh \left (6 c_1\right ) x^2\right )}{27 a^2 \sqrt [3]{4529848320 a^6 \cosh \left (6 c_1\right ) x^6+4529848320 a^6 \sinh \left (6 c_1\right ) x^6+1105920 a^3 \cosh \left (9 c_1\right ) x^3+1105920 a^3 \sinh \left (9 c_1\right ) x^3+432 \cosh \left (12 c_1\right )+432 \sinh \left (12 c_1\right )+\sqrt {-3361919107433565782016 a^{15} \cosh \left (9 c_1\right ) x^{15}-3361919107433565782016 a^{15} \sinh \left (9 c_1\right ) x^{15}+8207810320882728960 a^{12} \cosh \left (12 c_1\right ) x^{12}+8207810320882728960 a^{12} \sinh \left (12 c_1\right ) x^{12}-5009649854054400 a^9 \cosh \left (15 c_1\right ) x^9-5009649854054400 a^9 \sinh \left (15 c_1\right ) x^9-978447237120 a^6 \cosh \left (18 c_1\right ) x^6-978447237120 a^6 \sinh \left (18 c_1\right ) x^6+955514880 a^3 \cosh \left (21 c_1\right ) x^3+955514880 a^3 \sinh \left (21 c_1\right ) x^3+186624 \cosh \left (24 c_1\right )+186624 \sinh \left (24 c_1\right )}} x^2}+\frac {\left (1728 a^3 x^3-\cosh \left (3 c_1\right )-\sinh \left (3 c_1\right )\right ){}^2}{419904 a^4 x^4}}}+\frac {2 \cosh \left (3 c_1\right )}{81 a x}+\frac {2 \sinh \left (3 c_1\right )}{81 a x}-\frac {\sqrt [3]{4529848320 a^6 \cosh \left (6 c_1\right ) x^6+4529848320 a^6 \sinh \left (6 c_1\right ) x^6+1105920 a^3 \cosh \left (9 c_1\right ) x^3+1105920 a^3 \sinh \left (9 c_1\right ) x^3+432 \cosh \left (12 c_1\right )+432 \sinh \left (12 c_1\right )+\sqrt {-3361919107433565782016 a^{15} \cosh \left (9 c_1\right ) x^{15}-3361919107433565782016 a^{15} \sinh \left (9 c_1\right ) x^{15}+8207810320882728960 a^{12} \cosh \left (12 c_1\right ) x^{12}+8207810320882728960 a^{12} \sinh \left (12 c_1\right ) x^{12}-5009649854054400 a^9 \cosh \left (15 c_1\right ) x^9-5009649854054400 a^9 \sinh \left (15 c_1\right ) x^9-978447237120 a^6 \cosh \left (18 c_1\right ) x^6-978447237120 a^6 \sinh \left (18 c_1\right ) x^6+955514880 a^3 \cosh \left (21 c_1\right ) x^3+955514880 a^3 \sinh \left (21 c_1\right ) x^3+186624 \cosh \left (24 c_1\right )+186624 \sinh \left (24 c_1\right )}}}{3888 \sqrt [3]{2} a^2 x^2}-\frac {16 \sqrt [3]{2} \left (4096 a^5 \cosh \left (3 c_1\right ) x^5+4096 a^5 \sinh \left (3 c_1\right ) x^5+5 a^2 \cosh \left (6 c_1\right ) x^2+5 a^2 \sinh \left (6 c_1\right ) x^2\right )}{27 a^2 \sqrt [3]{4529848320 a^6 \cosh \left (6 c_1\right ) x^6+4529848320 a^6 \sinh \left (6 c_1\right ) x^6+1105920 a^3 \cosh \left (9 c_1\right ) x^3+1105920 a^3 \sinh \left (9 c_1\right ) x^3+432 \cosh \left (12 c_1\right )+432 \sinh \left (12 c_1\right )+\sqrt {-3361919107433565782016 a^{15} \cosh \left (9 c_1\right ) x^{15}-3361919107433565782016 a^{15} \sinh \left (9 c_1\right ) x^{15}+8207810320882728960 a^{12} \cosh \left (12 c_1\right ) x^{12}+8207810320882728960 a^{12} \sinh \left (12 c_1\right ) x^{12}-5009649854054400 a^9 \cosh \left (15 c_1\right ) x^9-5009649854054400 a^9 \sinh \left (15 c_1\right ) x^9-978447237120 a^6 \cosh \left (18 c_1\right ) x^6-978447237120 a^6 \sinh \left (18 c_1\right ) x^6+955514880 a^3 \cosh \left (21 c_1\right ) x^3+955514880 a^3 \sinh \left (21 c_1\right ) x^3+186624 \cosh \left (24 c_1\right )+186624 \sinh \left (24 c_1\right )}} x^2}+\frac {\left (1728 a^3 x^3-\cosh \left (3 c_1\right )-\sinh \left (3 c_1\right )\right ){}^2}{209952 a^4 x^4}}+\frac {\cosh \left (3 c_1\right )}{1296 a^2 x^2}+\frac {\sinh \left (3 c_1\right )}{1296 a^2 x^2}}\right \},\left \{y(x)\to \sqrt {-\frac {4 a x}{3}+\frac {1}{2} \sqrt {-\frac {64}{9} a^2 x^2+\frac {\cosh \left (3 c_1\right )}{81 a x}+\frac {\sinh \left (3 c_1\right )}{81 a x}+\frac {\sqrt [3]{4529848320 a^6 \cosh \left (6 c_1\right ) x^6+4529848320 a^6 \sinh \left (6 c_1\right ) x^6+1105920 a^3 \cosh \left (9 c_1\right ) x^3+1105920 a^3 \sinh \left (9 c_1\right ) x^3+432 \cosh \left (12 c_1\right )+432 \sinh \left (12 c_1\right )+\sqrt {-3361919107433565782016 a^{15} \cosh \left (9 c_1\right ) x^{15}-3361919107433565782016 a^{15} \sinh \left (9 c_1\right ) x^{15}+8207810320882728960 a^{12} \cosh \left (12 c_1\right ) x^{12}+8207810320882728960 a^{12} \sinh \left (12 c_1\right ) x^{12}-5009649854054400 a^9 \cosh \left (15 c_1\right ) x^9-5009649854054400 a^9 \sinh \left (15 c_1\right ) x^9-978447237120 a^6 \cosh \left (18 c_1\right ) x^6-978447237120 a^6 \sinh \left (18 c_1\right ) x^6+955514880 a^3 \cosh \left (21 c_1\right ) x^3+955514880 a^3 \sinh \left (21 c_1\right ) x^3+186624 \cosh \left (24 c_1\right )+186624 \sinh \left (24 c_1\right )}}}{3888 \sqrt [3]{2} a^2 x^2}+\frac {16 \sqrt [3]{2} \left (4096 a^5 \cosh \left (3 c_1\right ) x^5+4096 a^5 \sinh \left (3 c_1\right ) x^5+5 a^2 \cosh \left (6 c_1\right ) x^2+5 a^2 \sinh \left (6 c_1\right ) x^2\right )}{27 a^2 \sqrt [3]{4529848320 a^6 \cosh \left (6 c_1\right ) x^6+4529848320 a^6 \sinh \left (6 c_1\right ) x^6+1105920 a^3 \cosh \left (9 c_1\right ) x^3+1105920 a^3 \sinh \left (9 c_1\right ) x^3+432 \cosh \left (12 c_1\right )+432 \sinh \left (12 c_1\right )+\sqrt {-3361919107433565782016 a^{15} \cosh \left (9 c_1\right ) x^{15}-3361919107433565782016 a^{15} \sinh \left (9 c_1\right ) x^{15}+8207810320882728960 a^{12} \cosh \left (12 c_1\right ) x^{12}+8207810320882728960 a^{12} \sinh \left (12 c_1\right ) x^{12}-5009649854054400 a^9 \cosh \left (15 c_1\right ) x^9-5009649854054400 a^9 \sinh \left (15 c_1\right ) x^9-978447237120 a^6 \cosh \left (18 c_1\right ) x^6-978447237120 a^6 \sinh \left (18 c_1\right ) x^6+955514880 a^3 \cosh \left (21 c_1\right ) x^3+955514880 a^3 \sinh \left (21 c_1\right ) x^3+186624 \cosh \left (24 c_1\right )+186624 \sinh \left (24 c_1\right )}} x^2}+\frac {\left (1728 a^3 x^3-\cosh \left (3 c_1\right )-\sinh \left (3 c_1\right )\right ){}^2}{419904 a^4 x^4}}+\frac {1}{2} \sqrt {-\frac {128}{9} a^2 x^2+\frac {\frac {\cosh ^3\left (3 c_1\right )}{34012224 a^6 x^6}+\frac {\sinh \left (3 c_1\right ) \cosh ^2\left (3 c_1\right )}{11337408 a^6 x^6}+\frac {\cosh ^2\left (3 c_1\right )}{13122 a^3 x^3}+\frac {\sinh ^2\left (3 c_1\right ) \cosh \left (3 c_1\right )}{11337408 a^6 x^6}+\frac {\sinh \left (3 c_1\right ) \cosh \left (3 c_1\right )}{6561 a^3 x^3}+\frac {512}{243} \cosh \left (3 c_1\right )+\frac {\sinh ^3\left (3 c_1\right )}{34012224 a^6 x^6}+\frac {\sinh ^2\left (3 c_1\right )}{13122 a^3 x^3}+\frac {512}{243} \sinh \left (3 c_1\right )}{4 \sqrt {-\frac {64}{9} a^2 x^2+\frac {\cosh \left (3 c_1\right )}{81 a x}+\frac {\sinh \left (3 c_1\right )}{81 a x}+\frac {\sqrt [3]{4529848320 a^6 \cosh \left (6 c_1\right ) x^6+4529848320 a^6 \sinh \left (6 c_1\right ) x^6+1105920 a^3 \cosh \left (9 c_1\right ) x^3+1105920 a^3 \sinh \left (9 c_1\right ) x^3+432 \cosh \left (12 c_1\right )+432 \sinh \left (12 c_1\right )+\sqrt {-3361919107433565782016 a^{15} \cosh \left (9 c_1\right ) x^{15}-3361919107433565782016 a^{15} \sinh \left (9 c_1\right ) x^{15}+8207810320882728960 a^{12} \cosh \left (12 c_1\right ) x^{12}+8207810320882728960 a^{12} \sinh \left (12 c_1\right ) x^{12}-5009649854054400 a^9 \cosh \left (15 c_1\right ) x^9-5009649854054400 a^9 \sinh \left (15 c_1\right ) x^9-978447237120 a^6 \cosh \left (18 c_1\right ) x^6-978447237120 a^6 \sinh \left (18 c_1\right ) x^6+955514880 a^3 \cosh \left (21 c_1\right ) x^3+955514880 a^3 \sinh \left (21 c_1\right ) x^3+186624 \cosh \left (24 c_1\right )+186624 \sinh \left (24 c_1\right )}}}{3888 \sqrt [3]{2} a^2 x^2}+\frac {16 \sqrt [3]{2} \left (4096 a^5 \cosh \left (3 c_1\right ) x^5+4096 a^5 \sinh \left (3 c_1\right ) x^5+5 a^2 \cosh \left (6 c_1\right ) x^2+5 a^2 \sinh \left (6 c_1\right ) x^2\right )}{27 a^2 \sqrt [3]{4529848320 a^6 \cosh \left (6 c_1\right ) x^6+4529848320 a^6 \sinh \left (6 c_1\right ) x^6+1105920 a^3 \cosh \left (9 c_1\right ) x^3+1105920 a^3 \sinh \left (9 c_1\right ) x^3+432 \cosh \left (12 c_1\right )+432 \sinh \left (12 c_1\right )+\sqrt {-3361919107433565782016 a^{15} \cosh \left (9 c_1\right ) x^{15}-3361919107433565782016 a^{15} \sinh \left (9 c_1\right ) x^{15}+8207810320882728960 a^{12} \cosh \left (12 c_1\right ) x^{12}+8207810320882728960 a^{12} \sinh \left (12 c_1\right ) x^{12}-5009649854054400 a^9 \cosh \left (15 c_1\right ) x^9-5009649854054400 a^9 \sinh \left (15 c_1\right ) x^9-978447237120 a^6 \cosh \left (18 c_1\right ) x^6-978447237120 a^6 \sinh \left (18 c_1\right ) x^6+955514880 a^3 \cosh \left (21 c_1\right ) x^3+955514880 a^3 \sinh \left (21 c_1\right ) x^3+186624 \cosh \left (24 c_1\right )+186624 \sinh \left (24 c_1\right )}} x^2}+\frac {\left (1728 a^3 x^3-\cosh \left (3 c_1\right )-\sinh \left (3 c_1\right )\right ){}^2}{419904 a^4 x^4}}}+\frac {2 \cosh \left (3 c_1\right )}{81 a x}+\frac {2 \sinh \left (3 c_1\right )}{81 a x}-\frac {\sqrt [3]{4529848320 a^6 \cosh \left (6 c_1\right ) x^6+4529848320 a^6 \sinh \left (6 c_1\right ) x^6+1105920 a^3 \cosh \left (9 c_1\right ) x^3+1105920 a^3 \sinh \left (9 c_1\right ) x^3+432 \cosh \left (12 c_1\right )+432 \sinh \left (12 c_1\right )+\sqrt {-3361919107433565782016 a^{15} \cosh \left (9 c_1\right ) x^{15}-3361919107433565782016 a^{15} \sinh \left (9 c_1\right ) x^{15}+8207810320882728960 a^{12} \cosh \left (12 c_1\right ) x^{12}+8207810320882728960 a^{12} \sinh \left (12 c_1\right ) x^{12}-5009649854054400 a^9 \cosh \left (15 c_1\right ) x^9-5009649854054400 a^9 \sinh \left (15 c_1\right ) x^9-978447237120 a^6 \cosh \left (18 c_1\right ) x^6-978447237120 a^6 \sinh \left (18 c_1\right ) x^6+955514880 a^3 \cosh \left (21 c_1\right ) x^3+955514880 a^3 \sinh \left (21 c_1\right ) x^3+186624 \cosh \left (24 c_1\right )+186624 \sinh \left (24 c_1\right )}}}{3888 \sqrt [3]{2} a^2 x^2}-\frac {16 \sqrt [3]{2} \left (4096 a^5 \cosh \left (3 c_1\right ) x^5+4096 a^5 \sinh \left (3 c_1\right ) x^5+5 a^2 \cosh \left (6 c_1\right ) x^2+5 a^2 \sinh \left (6 c_1\right ) x^2\right )}{27 a^2 \sqrt [3]{4529848320 a^6 \cosh \left (6 c_1\right ) x^6+4529848320 a^6 \sinh \left (6 c_1\right ) x^6+1105920 a^3 \cosh \left (9 c_1\right ) x^3+1105920 a^3 \sinh \left (9 c_1\right ) x^3+432 \cosh \left (12 c_1\right )+432 \sinh \left (12 c_1\right )+\sqrt {-3361919107433565782016 a^{15} \cosh \left (9 c_1\right ) x^{15}-3361919107433565782016 a^{15} \sinh \left (9 c_1\right ) x^{15}+8207810320882728960 a^{12} \cosh \left (12 c_1\right ) x^{12}+8207810320882728960 a^{12} \sinh \left (12 c_1\right ) x^{12}-5009649854054400 a^9 \cosh \left (15 c_1\right ) x^9-5009649854054400 a^9 \sinh \left (15 c_1\right ) x^9-978447237120 a^6 \cosh \left (18 c_1\right ) x^6-978447237120 a^6 \sinh \left (18 c_1\right ) x^6+955514880 a^3 \cosh \left (21 c_1\right ) x^3+955514880 a^3 \sinh \left (21 c_1\right ) x^3+186624 \cosh \left (24 c_1\right )+186624 \sinh \left (24 c_1\right )}} x^2}+\frac {\left (1728 a^3 x^3-\cosh \left (3 c_1\right )-\sinh \left (3 c_1\right )\right ){}^2}{209952 a^4 x^4}}+\frac {\cosh \left (3 c_1\right )}{1296 a^2 x^2}+\frac {\sinh \left (3 c_1\right )}{1296 a^2 x^2}}\right \}\right \}\]
✓ Maple : cpu = 0.04 (sec), leaf count = 146
\[ \left \{ -{{\it \_C1}\,{x}^{2} \left ( {\frac {1}{x} \left ( -y \left ( x \right ) +\sqrt { \left ( y \left ( x \right ) \right ) ^{2}-4\,ax} \right ) } \right ) ^{{\frac {3}{2}}} \left ( -y \left ( x \right ) +\sqrt { \left ( y \left ( x \right ) \right ) ^{2}-4\,ax} \right ) ^{-2}}+x+{\frac {4\,a{x}^{2}}{3} \left ( -y \left ( x \right ) +\sqrt { \left ( y \left ( x \right ) \right ) ^{2}-4\,ax} \right ) ^{-2}}=0,{{\it \_C1}\,{x}^{2} \left ( {\frac {1}{x} \left ( -2\,y \left ( x \right ) -2\,\sqrt { \left ( y \left ( x \right ) \right ) ^{2}-4\,ax} \right ) } \right ) ^{{\frac {3}{2}}} \left ( y \left ( x \right ) +\sqrt { \left ( y \left ( x \right ) \right ) ^{2}-4\,ax} \right ) ^{-2}}+x+{\frac {4\,a{x}^{2}}{3} \left ( y \left ( x \right ) +\sqrt { \left ( y \left ( x \right ) \right ) ^{2}-4\,ax} \right ) ^{-2}}=0 \right \} \]