3.412   ODE No. 412

$$\boxed{{\displaystyle x{\left(\frac{\mathrm{d}}{\mathrm{d}x}y\left(x\right)\right)}^2+y\left(x\right)\frac{\mathrm{d}}{\mathrm{d}x}y\left(x\right)+a=0}}$$

1. Problem in Latex
2. Mathematica input
3. Maple input

Mathematica: cpu = 5.287171 (sec), leaf count = 16145 $$\{\{y(x)\to -\sqrt{-\frac{4ax}{3}-\frac{1}{2}\sqrt{-\frac{64}{9}{a}^2{x}^2+\frac{\cosh \left(3c_1\right)}{81ax}+\frac{\sinh \left(3c_1\right)}{81ax}+\frac{\sqrt[3]{4529848320a^6\cosh \left(6c_1\right)x^6+4529848320a^6\sinh \left(6c_1\right)x^6+1105920a^3\cosh \left(9c_1\right)x^3+1105920a^3\sinh \left(9c_1\right)x^3+432\cosh \left(12c_1\right)+432\sinh \left(12c_1\right)+\sqrt{-3361919107433565782016a^{15}\cosh \left(9c_1\right)x^{15}-3361919107433565782016a^{15}\sinh \left(9c_1\right)x^{15}+8207810320882728960a^{12}\cosh \left(12c_1\right)x^{12}+8207810320882728960a^{12}\sinh \left(12c_1\right)x^{12}-5009649854054400a^9\cosh \left(15c_1\right)x^9-5009649854054400a^9\sinh \left(15c_1\right)x^9-978447237120a^6\cosh \left(18c_1\right)x^6-978447237120a^6\sinh \left(18c_1\right)x^6+955514880a^3\cosh \left(21c_1\right)x^3+955514880a^3\sinh \left(21c_1\right)x^3+186624\cosh \left(24c_1\right)+186624\sinh \left(24c_1\right)}}}{3888\sqrt[3]{2}{a}^2{x}^2}+\frac{16\sqrt[3]{2}(4096a^5\cosh \left(3c_1\right)x^5+4096a^5\sinh \left(3c_1\right)x^5+5a^2\cosh \left(6c_1\right)x^2+5a^2\sinh \left(6c_1\right)x^2)}{27a^2\sqrt[3]{4529848320a^6\cosh \left(6c_1\right)x^6+4529848320a^6\sinh \left(6c_1\right)x^6+1105920a^3\cosh \left(9c_1\right)x^3+1105920a^3\sinh \left(9c_1\right)x^3+432\cosh \left(12c_1\right)+432\sinh \left(12c_1\right)+\sqrt{-3361919107433565782016a^{15}\cosh \left(9c_1\right)x^{15}-3361919107433565782016a^{15}\sinh \left(9c_1\right)x^{15}+8207810320882728960a^{12}\cosh \left(12c_1\right)x^{12}+8207810320882728960a^{12}\sinh \left(12c_1\right)x^{12}-5009649854054400a^9\cosh \left(15c_1\right)x^9-5009649854054400a^9\sinh \left(15c_1\right)x^9-978447237120a^6\cosh \left(18c_1\right)x^6-978447237120a^6\sinh \left(18c_1\right)x^6+955514880a^3\cosh \left(21c_1\right)x^3+955514880a^3\sinh \left(21c_1\right)x^3+186624\cosh \left(24c_1\right)+186624\sinh \left(24c_1\right)}}{x}^2}+\frac{(1728a^3{x}^3-\cosh \left(3c_1\right)-\sinh \left(3c_1\right)){}^2}{419904a^4{x}^4}}-\frac{1}{2}\sqrt{-\frac{128}{9}{a}^2{x}^2-\frac{\frac{{\cosh }^3\left(3c_1\right)}{34012224a^6{x}^6}+\frac{\sinh \left(3c_1\right){\cosh }^2\left(3c_1\right)}{11337408a^6{x}^6}+\frac{{\cosh }^2\left(3c_1\right)}{13122a^3{x}^3}+\frac{{\sinh }^2\left(3c_1\right)\cosh \left(3c_1\right)}{11337408a^6{x}^6}+\frac{\sinh \left(3c_1\right)\cosh \left(3c_1\right)}{6561a^3{x}^3}+\frac{512}{243}\cosh \left(3c_1\right)+\frac{{\sinh }^3\left(3c_1\right)}{34012224a^6{x}^6}+\frac{{\sinh }^2\left(3c_1\right)}{13122a^3{x}^3}+\frac{512}{243}\sinh \left(3c_1\right)}{4\sqrt{-\frac{64}{9}{a}^2{x}^2+\frac{\cosh \left(3c_1\right)}{81ax}+\frac{\sinh \left(3c_1\right)}{81ax}+\frac{\sqrt[3]{4529848320a^6\cosh \left(6c_1\right)x^6+4529848320a^6\sinh \left(6c_1\right)x^6+1105920a^3\cosh \left(9c_1\right)x^3+1105920a^3\sinh \left(9c_1\right)x^3+432\cosh \left(12c_1\right)+432\sinh \left(12c_1\right)+\sqrt{-3361919107433565782016a^{15}\cosh \left(9c_1\right)x^{15}-3361919107433565782016a^{15}\sinh \left(9c_1\right)x^{15}+8207810320882728960a^{12}\cosh \left(12c_1\right)x^{12}+8207810320882728960a^{12}\sinh \left(12c_1\right)x^{12}-5009649854054400a^9\cosh \left(15c_1\right)x^9-5009649854054400a^9\sinh \left(15c_1\right)x^9-978447237120a^6\cosh \left(18c_1\right)x^6-978447237120a^6\sinh \left(18c_1\right)x^6+955514880a^3\cosh \left(21c_1\right)x^3+955514880a^3\sinh \left(21c_1\right)x^3+186624\cosh \left(24c_1\right)+186624\sinh \left(24c_1\right)}}}{3888\sqrt[3]{2}{a}^2{x}^2}+\frac{16\sqrt[3]{2}(4096a^5\cosh \left(3c_1\right)x^5+4096a^5\sinh \left(3c_1\right)x^5+5a^2\cosh \left(6c_1\right)x^2+5a^2\sinh \left(6c_1\right)x^2)}{27a^2\sqrt[3]{4529848320a^6\cosh \left(6c_1\right)x^6+4529848320a^6\sinh \left(6c_1\right)x^6+1105920a^3\cosh \left(9c_1\right)x^3+1105920a^3\sinh \left(9c_1\right)x^3+432\cosh \left(12c_1\right)+432\sinh \left(12c_1\right)+\sqrt{-3361919107433565782016a^{15}\cosh \left(9c_1\right)x^{15}-3361919107433565782016a^{15}\sinh \left(9c_1\right)x^{15}+8207810320882728960a^{12}\cosh \left(12c_1\right)x^{12}+8207810320882728960a^{12}\sinh \left(12c_1\right)x^{12}-5009649854054400a^9\cosh \left(15c_1\right)x^9-5009649854054400a^9\sinh \left(15c_1\right)x^9-978447237120a^6\cosh \left(18c_1\right)x^6-978447237120a^6\sinh \left(18c_1\right)x^6+955514880a^3\cosh \left(21c_1\right)x^3+955514880a^3\sinh \left(21c_1\right)x^3+186624\cosh \left(24c_1\right)+186624\sinh \left(24c_1\right)}}{x}^2}+\frac{(1728a^3{x}^3-\cosh \left(3c_1\right)-\sinh \left(3c_1\right)){}^2}{419904a^4{x}^4}}}+\frac{2\cosh \left(3c_1\right)}{81ax}+\frac{2\sinh \left(3c_1\right)}{81ax}-\frac{\sqrt[3]{4529848320a^6\cosh \left(6c_1\right)x^6+4529848320a^6\sinh \left(6c_1\right)x^6+1105920a^3\cosh \left(9c_1\right)x^3+1105920a^3\sinh \left(9c_1\right)x^3+432\cosh \left(12c_1\right)+432\sinh \left(12c_1\right)+\sqrt{-3361919107433565782016a^{15}\cosh \left(9c_1\right)x^{15}-3361919107433565782016a^{15}\sinh \left(9c_1\right)x^{15}+8207810320882728960a^{12}\cosh \left(12c_1\right)x^{12}+8207810320882728960a^{12}\sinh \left(12c_1\right)x^{12}-5009649854054400a^9\cosh \left(15c_1\right)x^9-5009649854054400a^9\sinh \left(15c_1\right)x^9-978447237120a^6\cosh \left(18c_1\right)x^6-978447237120a^6\sinh \left(18c_1\right)x^6+955514880a^3\cosh \left(21c_1\right)x^3+955514880a^3\sinh \left(21c_1\right)x^3+186624\cosh \left(24c_1\right)+186624\sinh \left(24c_1\right)}}}{3888\sqrt[3]{2}{a}^2{x}^2}-\frac{16\sqrt[3]{2}(4096a^5\cosh \left(3c_1\right)x^5+4096a^5\sinh \left(3c_1\right)x^5+5a^2\cosh \left(6c_1\right)x^2+5a^2\sinh \left(6c_1\right)x^2)}{27a^2\sqrt[3]{4529848320a^6\cosh \left(6c_1\right)x^6+4529848320a^6\sinh \left(6c_1\right)x^6+1105920a^3\cosh \left(9c_1\right)x^3+1105920a^3\sinh \left(9c_1\right)x^3+432\cosh \left(12c_1\right)+432\sinh \left(12c_1\right)+\sqrt{-3361919107433565782016a^{15}\cosh \left(9c_1\right)x^{15}-3361919107433565782016a^{15}\sinh \left(9c_1\right)x^{15}+8207810320882728960a^{12}\cosh \left(12c_1\right)x^{12}+8207810320882728960a^{12}\sinh \left(12c_1\right)x^{12}-5009649854054400a^9\cosh \left(15c_1\right)x^9-5009649854054400a^9\sinh \left(15c_1\right)x^9-978447237120a^6\cosh \left(18c_1\right)x^6-978447237120a^6\sinh \left(18c_1\right)x^6+955514880a^3\cosh \left(21c_1\right)x^3+955514880a^3\sinh \left(21c_1\right)x^3+186624\cosh \left(24c_1\right)+186624\sinh \left(24c_1\right)}}{x}^2}+\frac{(1728a^3{x}^3-\cosh \left(3c_1\right)-\sinh \left(3c_1\right)){}^2}{209952a^4{x}^4}}+\frac{\cosh \left(3c_1\right)}{1296a^2{x}^2}+\frac{\sinh \left(3c_1\right)}{1296a^2{x}^2}}\},\{y(x)\to \sqrt{-\frac{4ax}{3}-\frac{1}{2}\sqrt{-\frac{64}{9}{a}^2{x}^2+\frac{\cosh \left(3c_1\right)}{81ax}+\frac{\sinh \left(3c_1\right)}{81ax}+\frac{\sqrt[3]{4529848320a^6\cosh \left(6c_1\right)x^6+4529848320a^6\sinh \left(6c_1\right)x^6+1105920a^3\cosh \left(9c_1\right)x^3+1105920a^3\sinh \left(9c_1\right)x^3+432\cosh \left(12c_1\right)+432\sinh \left(12c_1\right)+\sqrt{-3361919107433565782016a^{15}\cosh \left(9c_1\right)x^{15}-3361919107433565782016a^{15}\sinh \left(9c_1\right)x^{15}+8207810320882728960a^{12}\cosh \left(12c_1\right)x^{12}+8207810320882728960a^{12}\sinh \left(12c_1\right)x^{12}-5009649854054400a^9\cosh \left(15c_1\right)x^9-5009649854054400a^9\sinh \left(15c_1\right)x^9-978447237120a^6\cosh \left(18c_1\right)x^6-978447237120a^6\sinh \left(18c_1\right)x^6+955514880a^3\cosh \left(21c_1\right)x^3+955514880a^3\sinh \left(21c_1\right)x^3+186624\cosh \left(24c_1\right)+186624\sinh \left(24c_1\right)}}}{3888\sqrt[3]{2}{a}^2{x}^2}+\frac{16\sqrt[3]{2}(4096a^5\cosh \left(3c_1\right)x^5+4096a^5\sinh \left(3c_1\right)x^5+5a^2\cosh \left(6c_1\right)x^2+5a^2\sinh \left(6c_1\right)x^2)}{27a^2\sqrt[3]{4529848320a^6\cosh \left(6c_1\right)x^6+4529848320a^6\sinh \left(6c_1\right)x^6+1105920a^3\cosh \left(9c_1\right)x^3+1105920a^3\sinh \left(9c_1\right)x^3+432\cosh \left(12c_1\right)+432\sinh \left(12c_1\right)+\sqrt{-3361919107433565782016a^{15}\cosh \left(9c_1\right)x^{15}-3361919107433565782016a^{15}\sinh \left(9c_1\right)x^{15}+8207810320882728960a^{12}\cosh \left(12c_1\right)x^{12}+8207810320882728960a^{12}\sinh \left(12c_1\right)x^{12}-5009649854054400a^9\cosh \left(15c_1\right)x^9-5009649854054400a^9\sinh \left(15c_1\right)x^9-978447237120a^6\cosh \left(18c_1\right)x^6-978447237120a^6\sinh \left(18c_1\right)x^6+955514880a^3\cosh \left(21c_1\right)x^3+955514880a^3\sinh \left(21c_1\right)x^3+186624\cosh \left(24c_1\right)+186624\sinh \left(24c_1\right)}}{x}^2}+\frac{(1728a^3{x}^3-\cosh \left(3c_1\right)-\sinh \left(3c_1\right)){}^2}{419904a^4{x}^4}}-\frac{1}{2}\sqrt{-\frac{128}{9}{a}^2{x}^2-\frac{\frac{{\cosh }^3\left(3c_1\right)}{34012224a^6{x}^6}+\frac{\sinh \left(3c_1\right){\cosh }^2\left(3c_1\right)}{11337408a^6{x}^6}+\frac{{\cosh }^2\left(3c_1\right)}{13122a^3{x}^3}+\frac{{\sinh }^2\left(3c_1\right)\cosh \left(3c_1\right)}{11337408a^6{x}^6}+\frac{\sinh \left(3c_1\right)\cosh \left(3c_1\right)}{6561a^3{x}^3}+\frac{512}{243}\cosh \left(3c_1\right)+\frac{{\sinh }^3\left(3c_1\right)}{34012224a^6{x}^6}+\frac{{\sinh }^2\left(3c_1\right)}{13122a^3{x}^3}+\frac{512}{243}\sinh \left(3c_1\right)}{4\sqrt{-\frac{64}{9}{a}^2{x}^2+\frac{\cosh \left(3c_1\right)}{81ax}+\frac{\sinh \left(3c_1\right)}{81ax}+\frac{\sqrt[3]{4529848320a^6\cosh \left(6c_1\right)x^6+4529848320a^6\sinh \left(6c_1\right)x^6+1105920a^3\cosh \left(9c_1\right)x^3+1105920a^3\sinh \left(9c_1\right)x^3+432\cosh \left(12c_1\right)+432\sinh \left(12c_1\right)+\sqrt{-3361919107433565782016a^{15}\cosh \left(9c_1\right)x^{15}-3361919107433565782016a^{15}\sinh \left(9c_1\right)x^{15}+8207810320882728960a^{12}\cosh \left(12c_1\right)x^{12}+8207810320882728960a^{12}\sinh \left(12c_1\right)x^{12}-5009649854054400a^9\cosh \left(15c_1\right)x^9-5009649854054400a^9\sinh \left(15c_1\right)x^9-978447237120a^6\cosh \left(18c_1\right)x^6-978447237120a^6\sinh \left(18c_1\right)x^6+955514880a^3\cosh \left(21c_1\right)x^3+955514880a^3\sinh \left(21c_1\right)x^3+186624\cosh \left(24c_1\right)+186624\sinh \left(24c_1\right)}}}{3888\sqrt[3]{2}{a}^2{x}^2}+\frac{16\sqrt[3]{2}(4096a^5\cosh \left(3c_1\right)x^5+4096a^5\sinh \left(3c_1\right)x^5+5a^2\cosh \left(6c_1\right)x^2+5a^2\sinh \left(6c_1\right)x^2)}{27a^2\sqrt[3]{4529848320a^6\cosh \left(6c_1\right)x^6+4529848320a^6\sinh \left(6c_1\right)x^6+1105920a^3\cosh \left(9c_1\right)x^3+1105920a^3\sinh \left(9c_1\right)x^3+432\cosh \left(12c_1\right)+432\sinh \left(12c_1\right)+\sqrt{-3361919107433565782016a^{15}\cosh \left(9c_1\right)x^{15}-3361919107433565782016a^{15}\sinh \left(9c_1\right)x^{15}+8207810320882728960a^{12}\cosh \left(12c_1\right)x^{12}+8207810320882728960a^{12}\sinh \left(12c_1\right)x^{12}-5009649854054400a^9\cosh \left(15c_1\right)x^9-5009649854054400a^9\sinh \left(15c_1\right)x^9-978447237120a^6\cosh \left(18c_1\right)x^6-978447237120a^6\sinh \left(18c_1\right)x^6+955514880a^3\cosh \left(21c_1\right)x^3+955514880a^3\sinh \left(21c_1\right)x^3+186624\cosh \left(24c_1\right)+186624\sinh \left(24c_1\right)}}{x}^2}+\frac{(1728a^3{x}^3-\cosh \left(3c_1\right)-\sinh \left(3c_1\right)){}^2}{419904a^4{x}^4}}}+\frac{2\cosh \left(3c_1\right)}{81ax}+\frac{2\sinh \left(3c_1\right)}{81ax}-\frac{\sqrt[3]{4529848320a^6\cosh \left(6c_1\right)x^6+4529848320a^6\sinh \left(6c_1\right)x^6+1105920a^3\cosh \left(9c_1\right)x^3+1105920a^3\sinh \left(9c_1\right)x^3+432\cosh \left(12c_1\right)+432\sinh \left(12c_1\right)+\sqrt{-3361919107433565782016a^{15}\cosh \left(9c_1\right)x^{15}-3361919107433565782016a^{15}\sinh \left(9c_1\right)x^{15}+8207810320882728960a^{12}\cosh \left(12c_1\right)x^{12}+8207810320882728960a^{12}\sinh \left(12c_1\right)x^{12}-5009649854054400a^9\cosh \left(15c_1\right)x^9-5009649854054400a^9\sinh \left(15c_1\right)x^9-978447237120a^6\cosh \left(18c_1\right)x^6-978447237120a^6\sinh \left(18c_1\right)x^6+955514880a^3\cosh \left(21c_1\right)x^3+955514880a^3\sinh \left(21c_1\right)x^3+186624\cosh \left(24c_1\right)+186624\sinh \left(24c_1\right)}}}{3888\sqrt[3]{2}{a}^2{x}^2}-\frac{16\sqrt[3]{2}(4096a^5\cosh \left(3c_1\right)x^5+4096a^5\sinh \left(3c_1\right)x^5+5a^2\cosh \left(6c_1\right)x^2+5a^2\sinh \left(6c_1\right)x^2)}{27a^2\sqrt[3]{4529848320a^6\cosh \left(6c_1\right)x^6+4529848320a^6\sinh \left(6c_1\right)x^6+1105920a^3\cosh \left(9c_1\right)x^3+1105920a^3\sinh \left(9c_1\right)x^3+432\cosh \left(12c_1\right)+432\sinh \left(12c_1\right)+\sqrt{-3361919107433565782016a^{15}\cosh \left(9c_1\right)x^{15}-3361919107433565782016a^{15}\sinh \left(9c_1\right)x^{15}+8207810320882728960a^{12}\cosh \left(12c_1\right)x^{12}+8207810320882728960a^{12}\sinh \left(12c_1\right)x^{12}-5009649854054400a^9\cosh \left(15c_1\right)x^9-5009649854054400a^9\sinh \left(15c_1\right)x^9-978447237120a^6\cosh \left(18c_1\right)x^6-978447237120a^6\sinh \left(18c_1\right)x^6+955514880a^3\cosh \left(21c_1\right)x^3+955514880a^3\sinh \left(21c_1\right)x^3+186624\cosh \left(24c_1\right)+186624\sinh \left(24c_1\right)}}{x}^2}+\frac{(1728a^3{x}^3-\cosh \left(3c_1\right)-\sinh \left(3c_1\right)){}^2}{209952a^4{x}^4}}+\frac{\cosh \left(3c_1\right)}{1296a^2{x}^2}+\frac{\sinh \left(3c_1\right)}{1296a^2{x}^2}}\},\{y(x)\to -\sqrt{-\frac{4ax}{3}-\frac{1}{2}\sqrt{-\frac{64}{9}{a}^2{x}^2+\frac{\cosh \left(3c_1\right)}{81ax}+\frac{\sinh \left(3c_1\right)}{81ax}+\frac{\sqrt[3]{4529848320a^6\cosh \left(6c_1\right)x^6+4529848320a^6\sinh \left(6c_1\right)x^6+1105920a^3\cosh \left(9c_1\right)x^3+1105920a^3\sinh \left(9c_1\right)x^3+432\cosh \left(12c_1\right)+432\sinh \left(12c_1\right)+\sqrt{-3361919107433565782016a^{15}\cosh \left(9c_1\right)x^{15}-3361919107433565782016a^{15}\sinh \left(9c_1\right)x^{15}+8207810320882728960a^{12}\cosh \left(12c_1\right)x^{12}+8207810320882728960a^{12}\sinh \left(12c_1\right)x^{12}-5009649854054400a^9\cosh \left(15c_1\right)x^9-5009649854054400a^9\sinh \left(15c_1\right)x^9-978447237120a^6\cosh \left(18c_1\right)x^6-978447237120a^6\sinh \left(18c_1\right)x^6+955514880a^3\cosh \left(21c_1\right)x^3+955514880a^3\sinh \left(21c_1\right)x^3+186624\cosh \left(24c_1\right)+186624\sinh \left(24c_1\right)}}}{3888\sqrt[3]{2}{a}^2{x}^2}+\frac{16\sqrt[3]{2}(4096a^5\cosh \left(3c_1\right)x^5+4096a^5\sinh \left(3c_1\right)x^5+5a^2\cosh \left(6c_1\right)x^2+5a^2\sinh \left(6c_1\right)x^2)}{27a^2\sqrt[3]{4529848320a^6\cosh \left(6c_1\right)x^6+4529848320a^6\sinh \left(6c_1\right)x^6+1105920a^3\cosh \left(9c_1\right)x^3+1105920a^3\sinh \left(9c_1\right)x^3+432\cosh \left(12c_1\right)+432\sinh \left(12c_1\right)+\sqrt{-3361919107433565782016a^{15}\cosh \left(9c_1\right)x^{15}-3361919107433565782016a^{15}\sinh \left(9c_1\right)x^{15}+8207810320882728960a^{12}\cosh \left(12c_1\right)x^{12}+8207810320882728960a^{12}\sinh \left(12c_1\right)x^{12}-5009649854054400a^9\cosh \left(15c_1\right)x^9-5009649854054400a^9\sinh \left(15c_1\right)x^9-978447237120a^6\cosh \left(18c_1\right)x^6-978447237120a^6\sinh \left(18c_1\right)x^6+955514880a^3\cosh \left(21c_1\right)x^3+955514880a^3\sinh \left(21c_1\right)x^3+186624\cosh \left(24c_1\right)+186624\sinh \left(24c_1\right)}}{x}^2}+\frac{(1728a^3{x}^3-\cosh \left(3c_1\right)-\sinh \left(3c_1\right)){}^2}{419904a^4{x}^4}}+\frac{1}{2}\sqrt{-\frac{128}{9}{a}^2{x}^2-\frac{\frac{{\cosh }^3\left(3c_1\right)}{34012224a^6{x}^6}+\frac{\sinh \left(3c_1\right){\cosh }^2\left(3c_1\right)}{11337408a^6{x}^6}+\frac{{\cosh }^2\left(3c_1\right)}{13122a^3{x}^3}+\frac{{\sinh }^2\left(3c_1\right)\cosh \left(3c_1\right)}{11337408a^6{x}^6}+\frac{\sinh \left(3c_1\right)\cosh \left(3c_1\right)}{6561a^3{x}^3}+\frac{512}{243}\cosh \left(3c_1\right)+\frac{{\sinh }^3\left(3c_1\right)}{34012224a^6{x}^6}+\frac{{\sinh }^2\left(3c_1\right)}{13122a^3{x}^3}+\frac{512}{243}\sinh \left(3c_1\right)}{4\sqrt{-\frac{64}{9}{a}^2{x}^2+\frac{\cosh \left(3c_1\right)}{81ax}+\frac{\sinh \left(3c_1\right)}{81ax}+\frac{\sqrt[3]{4529848320a^6\cosh \left(6c_1\right)x^6+4529848320a^6\sinh \left(6c_1\right)x^6+1105920a^3\cosh \left(9c_1\right)x^3+1105920a^3\sinh \left(9c_1\right)x^3+432\cosh \left(12c_1\right)+432\sinh \left(12c_1\right)+\sqrt{-3361919107433565782016a^{15}\cosh \left(9c_1\right)x^{15}-3361919107433565782016a^{15}\sinh \left(9c_1\right)x^{15}+8207810320882728960a^{12}\cosh \left(12c_1\right)x^{12}+8207810320882728960a^{12}\sinh \left(12c_1\right)x^{12}-5009649854054400a^9\cosh \left(15c_1\right)x^9-5009649854054400a^9\sinh \left(15c_1\right)x^9-978447237120a^6\cosh \left(18c_1\right)x^6-978447237120a^6\sinh \left(18c_1\right)x^6+955514880a^3\cosh \left(21c_1\right)x^3+955514880a^3\sinh \left(21c_1\right)x^3+186624\cosh \left(24c_1\right)+186624\sinh \left(24c_1\right)}}}{3888\sqrt[3]{2}{a}^2{x}^2}+\frac{16\sqrt[3]{2}(4096a^5\cosh \left(3c_1\right)x^5+4096a^5\sinh \left(3c_1\right)x^5+5a^2\cosh \left(6c_1\right)x^2+5a^2\sinh \left(6c_1\right)x^2)}{27a^2\sqrt[3]{4529848320a^6\cosh \left(6c_1\right)x^6+4529848320a^6\sinh \left(6c_1\right)x^6+1105920a^3\cosh \left(9c_1\right)x^3+1105920a^3\sinh \left(9c_1\right)x^3+432\cosh \left(12c_1\right)+432\sinh \left(12c_1\right)+\sqrt{-3361919107433565782016a^{15}\cosh \left(9c_1\right)x^{15}-3361919107433565782016a^{15}\sinh \left(9c_1\right)x^{15}+8207810320882728960a^{12}\cosh \left(12c_1\right)x^{12}+8207810320882728960a^{12}\sinh \left(12c_1\right)x^{12}-5009649854054400a^9\cosh \left(15c_1\right)x^9-5009649854054400a^9\sinh \left(15c_1\right)x^9-978447237120a^6\cosh \left(18c_1\right)x^6-978447237120a^6\sinh \left(18c_1\right)x^6+955514880a^3\cosh \left(21c_1\right)x^3+955514880a^3\sinh \left(21c_1\right)x^3+186624\cosh \left(24c_1\right)+186624\sinh \left(24c_1\right)}}{x}^2}+\frac{(1728a^3{x}^3-\cosh \left(3c_1\right)-\sinh \left(3c_1\right)){}^2}{419904a^4{x}^4}}}+\frac{2\cosh \left(3c_1\right)}{81ax}+\frac{2\sinh \left(3c_1\right)}{81ax}-\frac{\sqrt[3]{4529848320a^6\cosh \left(6c_1\right)x^6+4529848320a^6\sinh \left(6c_1\right)x^6+1105920a^3\cosh \left(9c_1\right)x^3+1105920a^3\sinh \left(9c_1\right)x^3+432\cosh \left(12c_1\right)+432\sinh \left(12c_1\right)+\sqrt{-3361919107433565782016a^{15}\cosh \left(9c_1\right)x^{15}-3361919107433565782016a^{15}\sinh \left(9c_1\right)x^{15}+8207810320882728960a^{12}\cosh \left(12c_1\right)x^{12}+8207810320882728960a^{12}\sinh \left(12c_1\right)x^{12}-5009649854054400a^9\cosh \left(15c_1\right)x^9-5009649854054400a^9\sinh \left(15c_1\right)x^9-978447237120a^6\cosh \left(18c_1\right)x^6-978447237120a^6\sinh \left(18c_1\right)x^6+955514880a^3\cosh \left(21c_1\right)x^3+955514880a^3\sinh \left(21c_1\right)x^3+186624\cosh \left(24c_1\right)+186624\sinh \left(24c_1\right)}}}{3888\sqrt[3]{2}{a}^2{x}^2}-\frac{16\sqrt[3]{2}(4096a^5\cosh \left(3c_1\right)x^5+4096a^5\sinh \left(3c_1\right)x^5+5a^2\cosh \left(6c_1\right)x^2+5a^2\sinh \left(6c_1\right)x^2)}{27a^2\sqrt[3]{4529848320a^6\cosh \left(6c_1\right)x^6+4529848320a^6\sinh \left(6c_1\right)x^6+1105920a^3\cosh \left(9c_1\right)x^3+1105920a^3\sinh \left(9c_1\right)x^3+432\cosh \left(12c_1\right)+432\sinh \left(12c_1\right)+\sqrt{-3361919107433565782016a^{15}\cosh \left(9c_1\right)x^{15}-3361919107433565782016a^{15}\sinh \left(9c_1\right)x^{15}+8207810320882728960a^{12}\cosh \left(12c_1\right)x^{12}+8207810320882728960a^{12}\sinh \left(12c_1\right)x^{12}-5009649854054400a^9\cosh \left(15c_1\right)x^9-5009649854054400a^9\sinh \left(15c_1\right)x^9-978447237120a^6\cosh \left(18c_1\right)x^6-978447237120a^6\sinh \left(18c_1\right)x^6+955514880a^3\cosh \left(21c_1\right)x^3+955514880a^3\sinh \left(21c_1\right)x^3+186624\cosh \left(24c_1\right)+186624\sinh \left(24c_1\right)}}{x}^2}+\frac{(1728a^3{x}^3-\cosh \left(3c_1\right)-\sinh \left(3c_1\right)){}^2}{209952a^4{x}^4}}+\frac{\cosh \left(3c_1\right)}{1296a^2{x}^2}+\frac{\sinh \left(3c_1\right)}{1296a^2{x}^2}}\},\{y(x)\to \sqrt{-\frac{4ax}{3}-\frac{1}{2}\sqrt{-\frac{64}{9}{a}^2{x}^2+\frac{\cosh \left(3c_1\right)}{81ax}+\frac{\sinh \left(3c_1\right)}{81ax}+\frac{\sqrt[3]{4529848320a^6\cosh \left(6c_1\right)x^6+4529848320a^6\sinh \left(6c_1\right)x^6+1105920a^3\cosh \left(9c_1\right)x^3+1105920a^3\sinh \left(9c_1\right)x^3+432\cosh \left(12c_1\right)+432\sinh \left(12c_1\right)+\sqrt{-3361919107433565782016a^{15}\cosh \left(9c_1\right)x^{15}-3361919107433565782016a^{15}\sinh \left(9c_1\right)x^{15}+8207810320882728960a^{12}\cosh \left(12c_1\right)x^{12}+8207810320882728960a^{12}\sinh \left(12c_1\right)x^{12}-5009649854054400a^9\cosh \left(15c_1\right)x^9-5009649854054400a^9\sinh \left(15c_1\right)x^9-978447237120a^6\cosh \left(18c_1\right)x^6-978447237120a^6\sinh \left(18c_1\right)x^6+955514880a^3\cosh \left(21c_1\right)x^3+955514880a^3\sinh \left(21c_1\right)x^3+186624\cosh \left(24c_1\right)+186624\sinh \left(24c_1\right)}}}{3888\sqrt[3]{2}{a}^2{x}^2}+\frac{16\sqrt[3]{2}(4096a^5\cosh \left(3c_1\right)x^5+4096a^5\sinh \left(3c_1\right)x^5+5a^2\cosh \left(6c_1\right)x^2+5a^2\sinh \left(6c_1\right)x^2)}{27a^2\sqrt[3]{4529848320a^6\cosh \left(6c_1\right)x^6+4529848320a^6\sinh \left(6c_1\right)x^6+1105920a^3\cosh \left(9c_1\right)x^3+1105920a^3\sinh \left(9c_1\right)x^3+432\cosh \left(12c_1\right)+432\sinh \left(12c_1\right)+\sqrt{-3361919107433565782016a^{15}\cosh \left(9c_1\right)x^{15}-3361919107433565782016a^{15}\sinh \left(9c_1\right)x^{15}+8207810320882728960a^{12}\cosh \left(12c_1\right)x^{12}+8207810320882728960a^{12}\sinh \left(12c_1\right)x^{12}-5009649854054400a^9\cosh \left(15c_1\right)x^9-5009649854054400a^9\sinh \left(15c_1\right)x^9-978447237120a^6\cosh \left(18c_1\right)x^6-978447237120a^6\sinh \left(18c_1\right)x^6+955514880a^3\cosh \left(21c_1\right)x^3+955514880a^3\sinh \left(21c_1\right)x^3+186624\cosh \left(24c_1\right)+186624\sinh \left(24c_1\right)}}{x}^2}+\frac{(1728a^3{x}^3-\cosh \left(3c_1\right)-\sinh \left(3c_1\right)){}^2}{419904a^4{x}^4}}+\frac{1}{2}\sqrt{-\frac{128}{9}{a}^2{x}^2-\frac{\frac{{\cosh }^3\left(3c_1\right)}{34012224a^6{x}^6}+\frac{\sinh \left(3c_1\right){\cosh }^2\left(3c_1\right)}{11337408a^6{x}^6}+\frac{{\cosh }^2\left(3c_1\right)}{13122a^3{x}^3}+\frac{{\sinh }^2\left(3c_1\right)\cosh \left(3c_1\right)}{11337408a^6{x}^6}+\frac{\sinh \left(3c_1\right)\cosh \left(3c_1\right)}{6561a^3{x}^3}+\frac{512}{243}\cosh \left(3c_1\right)+\frac{{\sinh }^3\left(3c_1\right)}{34012224a^6{x}^6}+\frac{{\sinh }^2\left(3c_1\right)}{13122a^3{x}^3}+\frac{512}{243}\sinh \left(3c_1\right)}{4\sqrt{-\frac{64}{9}{a}^2{x}^2+\frac{\cosh \left(3c_1\right)}{81ax}+\frac{\sinh \left(3c_1\right)}{81ax}+\frac{\sqrt[3]{4529848320a^6\cosh \left(6c_1\right)x^6+4529848320a^6\sinh \left(6c_1\right)x^6+1105920a^3\cosh \left(9c_1\right)x^3+1105920a^3\sinh \left(9c_1\right)x^3+432\cosh \left(12c_1\right)+432\sinh \left(12c_1\right)+\sqrt{-3361919107433565782016a^{15}\cosh \left(9c_1\right)x^{15}-3361919107433565782016a^{15}\sinh \left(9c_1\right)x^{15}+8207810320882728960a^{12}\cosh \left(12c_1\right)x^{12}+8207810320882728960a^{12}\sinh \left(12c_1\right)x^{12}-5009649854054400a^9\cosh \left(15c_1\right)x^9-5009649854054400a^9\sinh \left(15c_1\right)x^9-978447237120a^6\cosh \left(18c_1\right)x^6-978447237120a^6\sinh \left(18c_1\right)x^6+955514880a^3\cosh \left(21c_1\right)x^3+955514880a^3\sinh \left(21c_1\right)x^3+186624\cosh \left(24c_1\right)+186624\sinh \left(24c_1\right)}}}{3888\sqrt[3]{2}{a}^2{x}^2}+\frac{16\sqrt[3]{2}(4096a^5\cosh \left(3c_1\right)x^5+4096a^5\sinh \left(3c_1\right)x^5+5a^2\cosh \left(6c_1\right)x^2+5a^2\sinh \left(6c_1\right)x^2)}{27a^2\sqrt[3]{4529848320a^6\cosh \left(6c_1\right)x^6+4529848320a^6\sinh \left(6c_1\right)x^6+1105920a^3\cosh \left(9c_1\right)x^3+1105920a^3\sinh \left(9c_1\right)x^3+432\cosh \left(12c_1\right)+432\sinh \left(12c_1\right)+\sqrt{-3361919107433565782016a^{15}\cosh \left(9c_1\right)x^{15}-3361919107433565782016a^{15}\sinh \left(9c_1\right)x^{15}+8207810320882728960a^{12}\cosh \left(12c_1\right)x^{12}+8207810320882728960a^{12}\sinh \left(12c_1\right)x^{12}-5009649854054400a^9\cosh \left(15c_1\right)x^9-5009649854054400a^9\sinh \left(15c_1\right)x^9-978447237120a^6\cosh \left(18c_1\right)x^6-978447237120a^6\sinh \left(18c_1\right)x^6+955514880a^3\cosh \left(21c_1\right)x^3+955514880a^3\sinh \left(21c_1\right)x^3+186624\cosh \left(24c_1\right)+186624\sinh \left(24c_1\right)}}{x}^2}+\frac{(1728a^3{x}^3-\cosh \left(3c_1\right)-\sinh \left(3c_1\right)){}^2}{419904a^4{x}^4}}}+\frac{2\cosh \left(3c_1\right)}{81ax}+\frac{2\sinh \left(3c_1\right)}{81ax}-\frac{\sqrt[3]{4529848320a^6\cosh \left(6c_1\right)x^6+4529848320a^6\sinh \left(6c_1\right)x^6+1105920a^3\cosh \left(9c_1\right)x^3+1105920a^3\sinh \left(9c_1\right)x^3+432\cosh \left(12c_1\right)+432\sinh \left(12c_1\right)+\sqrt{-3361919107433565782016a^{15}\cosh \left(9c_1\right)x^{15}-3361919107433565782016a^{15}\sinh \left(9c_1\right)x^{15}+8207810320882728960a^{12}\cosh \left(12c_1\right)x^{12}+8207810320882728960a^{12}\sinh \left(12c_1\right)x^{12}-5009649854054400a^9\cosh \left(15c_1\right)x^9-5009649854054400a^9\sinh \left(15c_1\right)x^9-978447237120a^6\cosh \left(18c_1\right)x^6-978447237120a^6\sinh \left(18c_1\right)x^6+955514880a^3\cosh \left(21c_1\right)x^3+955514880a^3\sinh \left(21c_1\right)x^3+186624\cosh \left(24c_1\right)+186624\sinh \left(24c_1\right)}}}{3888\sqrt[3]{2}{a}^2{x}^2}-\frac{16\sqrt[3]{2}(4096a^5\cosh \left(3c_1\right)x^5+4096a^5\sinh \left(3c_1\right)x^5+5a^2\cosh \left(6c_1\right)x^2+5a^2\sinh \left(6c_1\right)x^2)}{27a^2\sqrt[3]{4529848320a^6\cosh \left(6c_1\right)x^6+4529848320a^6\sinh \left(6c_1\right)x^6+1105920a^3\cosh \left(9c_1\right)x^3+1105920a^3\sinh \left(9c_1\right)x^3+432\cosh \left(12c_1\right)+432\sinh \left(12c_1\right)+\sqrt{-3361919107433565782016a^{15}\cosh \left(9c_1\right)x^{15}-3361919107433565782016a^{15}\sinh \left(9c_1\right)x^{15}+8207810320882728960a^{12}\cosh \left(12c_1\right)x^{12}+8207810320882728960a^{12}\sinh \left(12c_1\right)x^{12}-5009649854054400a^9\cosh \left(15c_1\right)x^9-5009649854054400a^9\sinh \left(15c_1\right)x^9-978447237120a^6\cosh \left(18c_1\right)x^6-978447237120a^6\sinh \left(18c_1\right)x^6+955514880a^3\cosh \left(21c_1\right)x^3+955514880a^3\sinh \left(21c_1\right)x^3+186624\cosh \left(24c_1\right)+186624\sinh \left(24c_1\right)}}{x}^2}+\frac{(1728a^3{x}^3-\cosh \left(3c_1\right)-\sinh \left(3c_1\right)){}^2}{209952a^4{x}^4}}+\frac{\cosh \left(3c_1\right)}{1296a^2{x}^2}+\frac{\sinh \left(3c_1\right)}{1296a^2{x}^2}}\},\{y(x)\to -\sqrt{-\frac{4ax}{3}+\frac{1}{2}\sqrt{-\frac{64}{9}{a}^2{x}^2+\frac{\cosh \left(3c_1\right)}{81ax}+\frac{\sinh \left(3c_1\right)}{81ax}+\frac{\sqrt[3]{4529848320a^6\cosh \left(6c_1\right)x^6+4529848320a^6\sinh \left(6c_1\right)x^6+1105920a^3\cosh \left(9c_1\right)x^3+1105920a^3\sinh \left(9c_1\right)x^3+432\cosh \left(12c_1\right)+432\sinh \left(12c_1\right)+\sqrt{-3361919107433565782016a^{15}\cosh \left(9c_1\right)x^{15}-3361919107433565782016a^{15}\sinh \left(9c_1\right)x^{15}+8207810320882728960a^{12}\cosh \left(12c_1\right)x^{12}+8207810320882728960a^{12}\sinh \left(12c_1\right)x^{12}-5009649854054400a^9\cosh \left(15c_1\right)x^9-5009649854054400a^9\sinh \left(15c_1\right)x^9-978447237120a^6\cosh \left(18c_1\right)x^6-978447237120a^6\sinh \left(18c_1\right)x^6+955514880a^3\cosh \left(21c_1\right)x^3+955514880a^3\sinh \left(21c_1\right)x^3+186624\cosh \left(24c_1\right)+186624\sinh \left(24c_1\right)}}}{3888\sqrt[3]{2}{a}^2{x}^2}+\frac{16\sqrt[3]{2}(4096a^5\cosh \left(3c_1\right)x^5+4096a^5\sinh \left(3c_1\right)x^5+5a^2\cosh \left(6c_1\right)x^2+5a^2\sinh \left(6c_1\right)x^2)}{27a^2\sqrt[3]{4529848320a^6\cosh \left(6c_1\right)x^6+4529848320a^6\sinh \left(6c_1\right)x^6+1105920a^3\cosh \left(9c_1\right)x^3+1105920a^3\sinh \left(9c_1\right)x^3+432\cosh \left(12c_1\right)+432\sinh \left(12c_1\right)+\sqrt{-3361919107433565782016a^{15}\cosh \left(9c_1\right)x^{15}-3361919107433565782016a^{15}\sinh \left(9c_1\right)x^{15}+8207810320882728960a^{12}\cosh \left(12c_1\right)x^{12}+8207810320882728960a^{12}\sinh \left(12c_1\right)x^{12}-5009649854054400a^9\cosh \left(15c_1\right)x^9-5009649854054400a^9\sinh \left(15c_1\right)x^9-978447237120a^6\cosh \left(18c_1\right)x^6-978447237120a^6\sinh \left(18c_1\right)x^6+955514880a^3\cosh \left(21c_1\right)x^3+955514880a^3\sinh \left(21c_1\right)x^3+186624\cosh \left(24c_1\right)+186624\sinh \left(24c_1\right)}}{x}^2}+\frac{(1728a^3{x}^3-\cosh \left(3c_1\right)-\sinh \left(3c_1\right)){}^2}{419904a^4{x}^4}}-\frac{1}{2}\sqrt{-\frac{128}{9}{a}^2{x}^2+\frac{\frac{{\cosh }^3\left(3c_1\right)}{34012224a^6{x}^6}+\frac{\sinh \left(3c_1\right){\cosh }^2\left(3c_1\right)}{11337408a^6{x}^6}+\frac{{\cosh }^2\left(3c_1\right)}{13122a^3{x}^3}+\frac{{\sinh }^2\left(3c_1\right)\cosh \left(3c_1\right)}{11337408a^6{x}^6}+\frac{\sinh \left(3c_1\right)\cosh \left(3c_1\right)}{6561a^3{x}^3}+\frac{512}{243}\cosh \left(3c_1\right)+\frac{{\sinh }^3\left(3c_1\right)}{34012224a^6{x}^6}+\frac{{\sinh }^2\left(3c_1\right)}{13122a^3{x}^3}+\frac{512}{243}\sinh \left(3c_1\right)}{4\sqrt{-\frac{64}{9}{a}^2{x}^2+\frac{\cosh \left(3c_1\right)}{81ax}+\frac{\sinh \left(3c_1\right)}{81ax}+\frac{\sqrt[3]{4529848320a^6\cosh \left(6c_1\right)x^6+4529848320a^6\sinh \left(6c_1\right)x^6+1105920a^3\cosh \left(9c_1\right)x^3+1105920a^3\sinh \left(9c_1\right)x^3+432\cosh \left(12c_1\right)+432\sinh \left(12c_1\right)+\sqrt{-3361919107433565782016a^{15}\cosh \left(9c_1\right)x^{15}-3361919107433565782016a^{15}\sinh \left(9c_1\right)x^{15}+8207810320882728960a^{12}\cosh \left(12c_1\right)x^{12}+8207810320882728960a^{12}\sinh \left(12c_1\right)x^{12}-5009649854054400a^9\cosh \left(15c_1\right)x^9-5009649854054400a^9\sinh \left(15c_1\right)x^9-978447237120a^6\cosh \left(18c_1\right)x^6-978447237120a^6\sinh \left(18c_1\right)x^6+955514880a^3\cosh \left(21c_1\right)x^3+955514880a^3\sinh \left(21c_1\right)x^3+186624\cosh \left(24c_1\right)+186624\sinh \left(24c_1\right)}}}{3888\sqrt[3]{2}{a}^2{x}^2}+\frac{16\sqrt[3]{2}(4096a^5\cosh \left(3c_1\right)x^5+4096a^5\sinh \left(3c_1\right)x^5+5a^2\cosh \left(6c_1\right)x^2+5a^2\sinh \left(6c_1\right)x^2)}{27a^2\sqrt[3]{4529848320a^6\cosh \left(6c_1\right)x^6+4529848320a^6\sinh \left(6c_1\right)x^6+1105920a^3\cosh \left(9c_1\right)x^3+1105920a^3\sinh \left(9c_1\right)x^3+432\cosh \left(12c_1\right)+432\sinh \left(12c_1\right)+\sqrt{-3361919107433565782016a^{15}\cosh \left(9c_1\right)x^{15}-3361919107433565782016a^{15}\sinh \left(9c_1\right)x^{15}+8207810320882728960a^{12}\cosh \left(12c_1\right)x^{12}+8207810320882728960a^{12}\sinh \left(12c_1\right)x^{12}-5009649854054400a^9\cosh \left(15c_1\right)x^9-5009649854054400a^9\sinh \left(15c_1\right)x^9-978447237120a^6\cosh \left(18c_1\right)x^6-978447237120a^6\sinh \left(18c_1\right)x^6+955514880a^3\cosh \left(21c_1\right)x^3+955514880a^3\sinh \left(21c_1\right)x^3+186624\cosh \left(24c_1\right)+186624\sinh \left(24c_1\right)}}{x}^2}+\frac{(1728a^3{x}^3-\cosh \left(3c_1\right)-\sinh \left(3c_1\right)){}^2}{419904a^4{x}^4}}}+\frac{2\cosh \left(3c_1\right)}{81ax}+\frac{2\sinh \left(3c_1\right)}{81ax}-\frac{\sqrt[3]{4529848320a^6\cosh \left(6c_1\right)x^6+4529848320a^6\sinh \left(6c_1\right)x^6+1105920a^3\cosh \left(9c_1\right)x^3+1105920a^3\sinh \left(9c_1\right)x^3+432\cosh \left(12c_1\right)+432\sinh \left(12c_1\right)+\sqrt{-3361919107433565782016a^{15}\cosh \left(9c_1\right)x^{15}-3361919107433565782016a^{15}\sinh \left(9c_1\right)x^{15}+8207810320882728960a^{12}\cosh \left(12c_1\right)x^{12}+8207810320882728960a^{12}\sinh \left(12c_1\right)x^{12}-5009649854054400a^9\cosh \left(15c_1\right)x^9-5009649854054400a^9\sinh \left(15c_1\right)x^9-978447237120a^6\cosh \left(18c_1\right)x^6-978447237120a^6\sinh \left(18c_1\right)x^6+955514880a^3\cosh \left(21c_1\right)x^3+955514880a^3\sinh \left(21c_1\right)x^3+186624\cosh \left(24c_1\right)+186624\sinh \left(24c_1\right)}}}{3888\sqrt[3]{2}{a}^2{x}^2}-\frac{16\sqrt[3]{2}(4096a^5\cosh \left(3c_1\right)x^5+4096a^5\sinh \left(3c_1\right)x^5+5a^2\cosh \left(6c_1\right)x^2+5a^2\sinh \left(6c_1\right)x^2)}{27a^2\sqrt[3]{4529848320a^6\cosh \left(6c_1\right)x^6+4529848320a^6\sinh \left(6c_1\right)x^6+1105920a^3\cosh \left(9c_1\right)x^3+1105920a^3\sinh \left(9c_1\right)x^3+432\cosh \left(12c_1\right)+432\sinh \left(12c_1\right)+\sqrt{-3361919107433565782016a^{15}\cosh \left(9c_1\right)x^{15}-3361919107433565782016a^{15}\sinh \left(9c_1\right)x^{15}+8207810320882728960a^{12}\cosh \left(12c_1\right)x^{12}+8207810320882728960a^{12}\sinh \left(12c_1\right)x^{12}-5009649854054400a^9\cosh \left(15c_1\right)x^9-5009649854054400a^9\sinh \left(15c_1\right)x^9-978447237120a^6\cosh \left(18c_1\right)x^6-978447237120a^6\sinh \left(18c_1\right)x^6+955514880a^3\cosh \left(21c_1\right)x^3+955514880a^3\sinh \left(21c_1\right)x^3+186624\cosh \left(24c_1\right)+186624\sinh \left(24c_1\right)}}{x}^2}+\frac{(1728a^3{x}^3-\cosh \left(3c_1\right)-\sinh \left(3c_1\right)){}^2}{209952a^4{x}^4}}+\frac{\cosh \left(3c_1\right)}{1296a^2{x}^2}+\frac{\sinh \left(3c_1\right)}{1296a^2{x}^2}}\},\{y(x)\to \sqrt{-\frac{4ax}{3}+\frac{1}{2}\sqrt{-\frac{64}{9}{a}^2{x}^2+\frac{\cosh \left(3c_1\right)}{81ax}+\frac{\sinh \left(3c_1\right)}{81ax}+\frac{\sqrt[3]{4529848320a^6\cosh \left(6c_1\right)x^6+4529848320a^6\sinh \left(6c_1\right)x^6+1105920a^3\cosh \left(9c_1\right)x^3+1105920a^3\sinh \left(9c_1\right)x^3+432\cosh \left(12c_1\right)+432\sinh \left(12c_1\right)+\sqrt{-3361919107433565782016a^{15}\cosh \left(9c_1\right)x^{15}-3361919107433565782016a^{15}\sinh \left(9c_1\right)x^{15}+8207810320882728960a^{12}\cosh \left(12c_1\right)x^{12}+8207810320882728960a^{12}\sinh \left(12c_1\right)x^{12}-5009649854054400a^9\cosh \left(15c_1\right)x^9-5009649854054400a^9\sinh \left(15c_1\right)x^9-978447237120a^6\cosh \left(18c_1\right)x^6-978447237120a^6\sinh \left(18c_1\right)x^6+955514880a^3\cosh \left(21c_1\right)x^3+955514880a^3\sinh \left(21c_1\right)x^3+186624\cosh \left(24c_1\right)+186624\sinh \left(24c_1\right)}}}{3888\sqrt[3]{2}{a}^2{x}^2}+\frac{16\sqrt[3]{2}(4096a^5\cosh \left(3c_1\right)x^5+4096a^5\sinh \left(3c_1\right)x^5+5a^2\cosh \left(6c_1\right)x^2+5a^2\sinh \left(6c_1\right)x^2)}{27a^2\sqrt[3]{4529848320a^6\cosh \left(6c_1\right)x^6+4529848320a^6\sinh \left(6c_1\right)x^6+1105920a^3\cosh \left(9c_1\right)x^3+1105920a^3\sinh \left(9c_1\right)x^3+432\cosh \left(12c_1\right)+432\sinh \left(12c_1\right)+\sqrt{-3361919107433565782016a^{15}\cosh \left(9c_1\right)x^{15}-3361919107433565782016a^{15}\sinh \left(9c_1\right)x^{15}+8207810320882728960a^{12}\cosh \left(12c_1\right)x^{12}+8207810320882728960a^{12}\sinh \left(12c_1\right)x^{12}-5009649854054400a^9\cosh \left(15c_1\right)x^9-5009649854054400a^9\sinh \left(15c_1\right)x^9-978447237120a^6\cosh \left(18c_1\right)x^6-978447237120a^6\sinh \left(18c_1\right)x^6+955514880a^3\cosh \left(21c_1\right)x^3+955514880a^3\sinh \left(21c_1\right)x^3+186624\cosh \left(24c_1\right)+186624\sinh \left(24c_1\right)}}{x}^2}+\frac{(1728a^3{x}^3-\cosh \left(3c_1\right)-\sinh \left(3c_1\right)){}^2}{419904a^4{x}^4}}-\frac{1}{2}\sqrt{-\frac{128}{9}{a}^2{x}^2+\frac{\frac{{\cosh }^3\left(3c_1\right)}{34012224a^6{x}^6}+\frac{\sinh \left(3c_1\right){\cosh }^2\left(3c_1\right)}{11337408a^6{x}^6}+\frac{{\cosh }^2\left(3c_1\right)}{13122a^3{x}^3}+\frac{{\sinh }^2\left(3c_1\right)\cosh \left(3c_1\right)}{11337408a^6{x}^6}+\frac{\sinh \left(3c_1\right)\cosh \left(3c_1\right)}{6561a^3{x}^3}+\frac{512}{243}\cosh \left(3c_1\right)+\frac{{\sinh }^3\left(3c_1\right)}{34012224a^6{x}^6}+\frac{{\sinh }^2\left(3c_1\right)}{13122a^3{x}^3}+\frac{512}{243}\sinh \left(3c_1\right)}{4\sqrt{-\frac{64}{9}{a}^2{x}^2+\frac{\cosh \left(3c_1\right)}{81ax}+\frac{\sinh \left(3c_1\right)}{81ax}+\frac{\sqrt[3]{4529848320a^6\cosh \left(6c_1\right)x^6+4529848320a^6\sinh \left(6c_1\right)x^6+1105920a^3\cosh \left(9c_1\right)x^3+1105920a^3\sinh \left(9c_1\right)x^3+432\cosh \left(12c_1\right)+432\sinh \left(12c_1\right)+\sqrt{-3361919107433565782016a^{15}\cosh \left(9c_1\right)x^{15}-3361919107433565782016a^{15}\sinh \left(9c_1\right)x^{15}+8207810320882728960a^{12}\cosh \left(12c_1\right)x^{12}+8207810320882728960a^{12}\sinh \left(12c_1\right)x^{12}-5009649854054400a^9\cosh \left(15c_1\right)x^9-5009649854054400a^9\sinh \left(15c_1\right)x^9-978447237120a^6\cosh \left(18c_1\right)x^6-978447237120a^6\sinh \left(18c_1\right)x^6+955514880a^3\cosh \left(21c_1\right)x^3+955514880a^3\sinh \left(21c_1\right)x^3+186624\cosh \left(24c_1\right)+186624\sinh \left(24c_1\right)}}}{3888\sqrt[3]{2}{a}^2{x}^2}+\frac{16\sqrt[3]{2}(4096a^5\cosh \left(3c_1\right)x^5+4096a^5\sinh \left(3c_1\right)x^5+5a^2\cosh \left(6c_1\right)x^2+5a^2\sinh \left(6c_1\right)x^2)}{27a^2\sqrt[3]{4529848320a^6\cosh \left(6c_1\right)x^6+4529848320a^6\sinh \left(6c_1\right)x^6+1105920a^3\cosh \left(9c_1\right)x^3+1105920a^3\sinh \left(9c_1\right)x^3+432\cosh \left(12c_1\right)+432\sinh \left(12c_1\right)+\sqrt{-3361919107433565782016a^{15}\cosh \left(9c_1\right)x^{15}-3361919107433565782016a^{15}\sinh \left(9c_1\right)x^{15}+8207810320882728960a^{12}\cosh \left(12c_1\right)x^{12}+8207810320882728960a^{12}\sinh \left(12c_1\right)x^{12}-5009649854054400a^9\cosh \left(15c_1\right)x^9-5009649854054400a^9\sinh \left(15c_1\right)x^9-978447237120a^6\cosh \left(18c_1\right)x^6-978447237120a^6\sinh \left(18c_1\right)x^6+955514880a^3\cosh \left(21c_1\right)x^3+955514880a^3\sinh \left(21c_1\right)x^3+186624\cosh \left(24c_1\right)+186624\sinh \left(24c_1\right)}}{x}^2}+\frac{(1728a^3{x}^3-\cosh \left(3c_1\right)-\sinh \left(3c_1\right)){}^2}{419904a^4{x}^4}}}+\frac{2\cosh \left(3c_1\right)}{81ax}+\frac{2\sinh \left(3c_1\right)}{81ax}-\frac{\sqrt[3]{4529848320a^6\cosh \left(6c_1\right)x^6+4529848320a^6\sinh \left(6c_1\right)x^6+1105920a^3\cosh \left(9c_1\right)x^3+1105920a^3\sinh \left(9c_1\right)x^3+432\cosh \left(12c_1\right)+432\sinh \left(12c_1\right)+\sqrt{-3361919107433565782016a^{15}\cosh \left(9c_1\right)x^{15}-3361919107433565782016a^{15}\sinh \left(9c_1\right)x^{15}+8207810320882728960a^{12}\cosh \left(12c_1\right)x^{12}+8207810320882728960a^{12}\sinh \left(12c_1\right)x^{12}-5009649854054400a^9\cosh \left(15c_1\right)x^9-5009649854054400a^9\sinh \left(15c_1\right)x^9-978447237120a^6\cosh \left(18c_1\right)x^6-978447237120a^6\sinh \left(18c_1\right)x^6+955514880a^3\cosh \left(21c_1\right)x^3+955514880a^3\sinh \left(21c_1\right)x^3+186624\cosh \left(24c_1\right)+186624\sinh \left(24c_1\right)}}}{3888\sqrt[3]{2}{a}^2{x}^2}-\frac{16\sqrt[3]{2}(4096a^5\cosh \left(3c_1\right)x^5+4096a^5\sinh \left(3c_1\right)x^5+5a^2\cosh \left(6c_1\right)x^2+5a^2\sinh \left(6c_1\right)x^2)}{27a^2\sqrt[3]{4529848320a^6\cosh \left(6c_1\right)x^6+4529848320a^6\sinh \left(6c_1\right)x^6+1105920a^3\cosh \left(9c_1\right)x^3+1105920a^3\sinh \left(9c_1\right)x^3+432\cosh \left(12c_1\right)+432\sinh \left(12c_1\right)+\sqrt{-3361919107433565782016a^{15}\cosh \left(9c_1\right)x^{15}-3361919107433565782016a^{15}\sinh \left(9c_1\right)x^{15}+8207810320882728960a^{12}\cosh \left(12c_1\right)x^{12}+8207810320882728960a^{12}\sinh \left(12c_1\right)x^{12}-5009649854054400a^9\cosh \left(15c_1\right)x^9-5009649854054400a^9\sinh \left(15c_1\right)x^9-978447237120a^6\cosh \left(18c_1\right)x^6-978447237120a^6\sinh \left(18c_1\right)x^6+955514880a^3\cosh \left(21c_1\right)x^3+955514880a^3\sinh \left(21c_1\right)x^3+186624\cosh \left(24c_1\right)+186624\sinh \left(24c_1\right)}}{x}^2}+\frac{(1728a^3{x}^3-\cosh \left(3c_1\right)-\sinh \left(3c_1\right)){}^2}{209952a^4{x}^4}}+\frac{\cosh \left(3c_1\right)}{1296a^2{x}^2}+\frac{\sinh \left(3c_1\right)}{1296a^2{x}^2}}\},\{y(x)\to -\sqrt{-\frac{4ax}{3}+\frac{1}{2}\sqrt{-\frac{64}{9}{a}^2{x}^2+\frac{\cosh \left(3c_1\right)}{81ax}+\frac{\sinh \left(3c_1\right)}{81ax}+\frac{\sqrt[3]{4529848320a^6\cosh \left(6c_1\right)x^6+4529848320a^6\sinh \left(6c_1\right)x^6+1105920a^3\cosh \left(9c_1\right)x^3+1105920a^3\sinh \left(9c_1\right)x^3+432\cosh \left(12c_1\right)+432\sinh \left(12c_1\right)+\sqrt{-3361919107433565782016a^{15}\cosh \left(9c_1\right)x^{15}-3361919107433565782016a^{15}\sinh \left(9c_1\right)x^{15}+8207810320882728960a^{12}\cosh \left(12c_1\right)x^{12}+8207810320882728960a^{12}\sinh \left(12c_1\right)x^{12}-5009649854054400a^9\cosh \left(15c_1\right)x^9-5009649854054400a^9\sinh \left(15c_1\right)x^9-978447237120a^6\cosh \left(18c_1\right)x^6-978447237120a^6\sinh \left(18c_1\right)x^6+955514880a^3\cosh \left(21c_1\right)x^3+955514880a^3\sinh \left(21c_1\right)x^3+186624\cosh \left(24c_1\right)+186624\sinh \left(24c_1\right)}}}{3888\sqrt[3]{2}{a}^2{x}^2}+\frac{16\sqrt[3]{2}(4096a^5\cosh \left(3c_1\right)x^5+4096a^5\sinh \left(3c_1\right)x^5+5a^2\cosh \left(6c_1\right)x^2+5a^2\sinh \left(6c_1\right)x^2)}{27a^2\sqrt[3]{4529848320a^6\cosh \left(6c_1\right)x^6+4529848320a^6\sinh \left(6c_1\right)x^6+1105920a^3\cosh \left(9c_1\right)x^3+1105920a^3\sinh \left(9c_1\right)x^3+432\cosh \left(12c_1\right)+432\sinh \left(12c_1\right)+\sqrt{-3361919107433565782016a^{15}\cosh \left(9c_1\right)x^{15}-3361919107433565782016a^{15}\sinh \left(9c_1\right)x^{15}+8207810320882728960a^{12}\cosh \left(12c_1\right)x^{12}+8207810320882728960a^{12}\sinh \left(12c_1\right)x^{12}-5009649854054400a^9\cosh \left(15c_1\right)x^9-5009649854054400a^9\sinh \left(15c_1\right)x^9-978447237120a^6\cosh \left(18c_1\right)x^6-978447237120a^6\sinh \left(18c_1\right)x^6+955514880a^3\cosh \left(21c_1\right)x^3+955514880a^3\sinh \left(21c_1\right)x^3+186624\cosh \left(24c_1\right)+186624\sinh \left(24c_1\right)}}{x}^2}+\frac{(1728a^3{x}^3-\cosh \left(3c_1\right)-\sinh \left(3c_1\right)){}^2}{419904a^4{x}^4}}+\frac{1}{2}\sqrt{-\frac{128}{9}{a}^2{x}^2+\frac{\frac{{\cosh }^3\left(3c_1\right)}{34012224a^6{x}^6}+\frac{\sinh \left(3c_1\right){\cosh }^2\left(3c_1\right)}{11337408a^6{x}^6}+\frac{{\cosh }^2\left(3c_1\right)}{13122a^3{x}^3}+\frac{{\sinh }^2\left(3c_1\right)\cosh \left(3c_1\right)}{11337408a^6{x}^6}+\frac{\sinh \left(3c_1\right)\cosh \left(3c_1\right)}{6561a^3{x}^3}+\frac{512}{243}\cosh \left(3c_1\right)+\frac{{\sinh }^3\left(3c_1\right)}{34012224a^6{x}^6}+\frac{{\sinh }^2\left(3c_1\right)}{13122a^3{x}^3}+\frac{512}{243}\sinh \left(3c_1\right)}{4\sqrt{-\frac{64}{9}{a}^2{x}^2+\frac{\cosh \left(3c_1\right)}{81ax}+\frac{\sinh \left(3c_1\right)}{81ax}+\frac{\sqrt[3]{4529848320a^6\cosh \left(6c_1\right)x^6+4529848320a^6\sinh \left(6c_1\right)x^6+1105920a^3\cosh \left(9c_1\right)x^3+1105920a^3\sinh \left(9c_1\right)x^3+432\cosh \left(12c_1\right)+432\sinh \left(12c_1\right)+\sqrt{-3361919107433565782016a^{15}\cosh \left(9c_1\right)x^{15}-3361919107433565782016a^{15}\sinh \left(9c_1\right)x^{15}+8207810320882728960a^{12}\cosh \left(12c_1\right)x^{12}+8207810320882728960a^{12}\sinh \left(12c_1\right)x^{12}-5009649854054400a^9\cosh \left(15c_1\right)x^9-5009649854054400a^9\sinh \left(15c_1\right)x^9-978447237120a^6\cosh \left(18c_1\right)x^6-978447237120a^6\sinh \left(18c_1\right)x^6+955514880a^3\cosh \left(21c_1\right)x^3+955514880a^3\sinh \left(21c_1\right)x^3+186624\cosh \left(24c_1\right)+186624\sinh \left(24c_1\right)}}}{3888\sqrt[3]{2}{a}^2{x}^2}+\frac{16\sqrt[3]{2}(4096a^5\cosh \left(3c_1\right)x^5+4096a^5\sinh \left(3c_1\right)x^5+5a^2\cosh \left(6c_1\right)x^2+5a^2\sinh \left(6c_1\right)x^2)}{27a^2\sqrt[3]{4529848320a^6\cosh \left(6c_1\right)x^6+4529848320a^6\sinh \left(6c_1\right)x^6+1105920a^3\cosh \left(9c_1\right)x^3+1105920a^3\sinh \left(9c_1\right)x^3+432\cosh \left(12c_1\right)+432\sinh \left(12c_1\right)+\sqrt{-3361919107433565782016a^{15}\cosh \left(9c_1\right)x^{15}-3361919107433565782016a^{15}\sinh \left(9c_1\right)x^{15}+8207810320882728960a^{12}\cosh \left(12c_1\right)x^{12}+8207810320882728960a^{12}\sinh \left(12c_1\right)x^{12}-5009649854054400a^9\cosh \left(15c_1\right)x^9-5009649854054400a^9\sinh \left(15c_1\right)x^9-978447237120a^6\cosh \left(18c_1\right)x^6-978447237120a^6\sinh \left(18c_1\right)x^6+955514880a^3\cosh \left(21c_1\right)x^3+955514880a^3\sinh \left(21c_1\right)x^3+186624\cosh \left(24c_1\right)+186624\sinh \left(24c_1\right)}}{x}^2}+\frac{(1728a^3{x}^3-\cosh \left(3c_1\right)-\sinh \left(3c_1\right)){}^2}{419904a^4{x}^4}}}+\frac{2\cosh \left(3c_1\right)}{81ax}+\frac{2\sinh \left(3c_1\right)}{81ax}-\frac{\sqrt[3]{4529848320a^6\cosh \left(6c_1\right)x^6+4529848320a^6\sinh \left(6c_1\right)x^6+1105920a^3\cosh \left(9c_1\right)x^3+1105920a^3\sinh \left(9c_1\right)x^3+432\cosh \left(12c_1\right)+432\sinh \left(12c_1\right)+\sqrt{-3361919107433565782016a^{15}\cosh \left(9c_1\right)x^{15}-3361919107433565782016a^{15}\sinh \left(9c_1\right)x^{15}+8207810320882728960a^{12}\cosh \left(12c_1\right)x^{12}+8207810320882728960a^{12}\sinh \left(12c_1\right)x^{12}-5009649854054400a^9\cosh \left(15c_1\right)x^9-5009649854054400a^9\sinh \left(15c_1\right)x^9-978447237120a^6\cosh \left(18c_1\right)x^6-978447237120a^6\sinh \left(18c_1\right)x^6+955514880a^3\cosh \left(21c_1\right)x^3+955514880a^3\sinh \left(21c_1\right)x^3+186624\cosh \left(24c_1\right)+186624\sinh \left(24c_1\right)}}}{3888\sqrt[3]{2}{a}^2{x}^2}-\frac{16\sqrt[3]{2}(4096a^5\cosh \left(3c_1\right)x^5+4096a^5\sinh \left(3c_1\right)x^5+5a^2\cosh \left(6c_1\right)x^2+5a^2\sinh \left(6c_1\right)x^2)}{27a^2\sqrt[3]{4529848320a^6\cosh \left(6c_1\right)x^6+4529848320a^6\sinh \left(6c_1\right)x^6+1105920a^3\cosh \left(9c_1\right)x^3+1105920a^3\sinh \left(9c_1\right)x^3+432\cosh \left(12c_1\right)+432\sinh \left(12c_1\right)+\sqrt{-3361919107433565782016a^{15}\cosh \left(9c_1\right)x^{15}-3361919107433565782016a^{15}\sinh \left(9c_1\right)x^{15}+8207810320882728960a^{12}\cosh \left(12c_1\right)x^{12}+8207810320882728960a^{12}\sinh \left(12c_1\right)x^{12}-5009649854054400a^9\cosh \left(15c_1\right)x^9-5009649854054400a^9\sinh \left(15c_1\right)x^9-978447237120a^6\cosh \left(18c_1\right)x^6-978447237120a^6\sinh \left(18c_1\right)x^6+955514880a^3\cosh \left(21c_1\right)x^3+955514880a^3\sinh \left(21c_1\right)x^3+186624\cosh \left(24c_1\right)+186624\sinh \left(24c_1\right)}}{x}^2}+\frac{(1728a^3{x}^3-\cosh \left(3c_1\right)-\sinh \left(3c_1\right)){}^2}{209952a^4{x}^4}}+\frac{\cosh \left(3c_1\right)}{1296a^2{x}^2}+\frac{\sinh \left(3c_1\right)}{1296a^2{x}^2}}\},\{y(x)\to \sqrt{-\frac{4ax}{3}+\frac{1}{2}\sqrt{-\frac{64}{9}{a}^2{x}^2+\frac{\cosh \left(3c_1\right)}{81ax}+\frac{\sinh \left(3c_1\right)}{81ax}+\frac{\sqrt[3]{4529848320a^6\cosh \left(6c_1\right)x^6+4529848320a^6\sinh \left(6c_1\right)x^6+1105920a^3\cosh \left(9c_1\right)x^3+1105920a^3\sinh \left(9c_1\right)x^3+432\cosh \left(12c_1\right)+432\sinh \left(12c_1\right)+\sqrt{-3361919107433565782016a^{15}\cosh \left(9c_1\right)x^{15}-3361919107433565782016a^{15}\sinh \left(9c_1\right)x^{15}+8207810320882728960a^{12}\cosh \left(12c_1\right)x^{12}+8207810320882728960a^{12}\sinh \left(12c_1\right)x^{12}-5009649854054400a^9\cosh \left(15c_1\right)x^9-5009649854054400a^9\sinh \left(15c_1\right)x^9-978447237120a^6\cosh \left(18c_1\right)x^6-978447237120a^6\sinh \left(18c_1\right)x^6+955514880a^3\cosh \left(21c_1\right)x^3+955514880a^3\sinh \left(21c_1\right)x^3+186624\cosh \left(24c_1\right)+186624\sinh \left(24c_1\right)}}}{3888\sqrt[3]{2}{a}^2{x}^2}+\frac{16\sqrt[3]{2}(4096a^5\cosh \left(3c_1\right)x^5+4096a^5\sinh \left(3c_1\right)x^5+5a^2\cosh \left(6c_1\right)x^2+5a^2\sinh \left(6c_1\right)x^2)}{27a^2\sqrt[3]{4529848320a^6\cosh \left(6c_1\right)x^6+4529848320a^6\sinh \left(6c_1\right)x^6+1105920a^3\cosh \left(9c_1\right)x^3+1105920a^3\sinh \left(9c_1\right)x^3+432\cosh \left(12c_1\right)+432\sinh \left(12c_1\right)+\sqrt{-3361919107433565782016a^{15}\cosh \left(9c_1\right)x^{15}-3361919107433565782016a^{15}\sinh \left(9c_1\right)x^{15}+8207810320882728960a^{12}\cosh \left(12c_1\right)x^{12}+8207810320882728960a^{12}\sinh \left(12c_1\right)x^{12}-5009649854054400a^9\cosh \left(15c_1\right)x^9-5009649854054400a^9\sinh \left(15c_1\right)x^9-978447237120a^6\cosh \left(18c_1\right)x^6-978447237120a^6\sinh \left(18c_1\right)x^6+955514880a^3\cosh \left(21c_1\right)x^3+955514880a^3\sinh \left(21c_1\right)x^3+186624\cosh \left(24c_1\right)+186624\sinh \left(24c_1\right)}}{x}^2}+\frac{(1728a^3{x}^3-\cosh \left(3c_1\right)-\sinh \left(3c_1\right)){}^2}{419904a^4{x}^4}}+\frac{1}{2}\sqrt{-\frac{128}{9}{a}^2{x}^2+\frac{\frac{{\cosh }^3\left(3c_1\right)}{34012224a^6{x}^6}+\frac{\sinh \left(3c_1\right){\cosh }^2\left(3c_1\right)}{11337408a^6{x}^6}+\frac{{\cosh }^2\left(3c_1\right)}{13122a^3{x}^3}+\frac{{\sinh }^2\left(3c_1\right)\cosh \left(3c_1\right)}{11337408a^6{x}^6}+\frac{\sinh \left(3c_1\right)\cosh \left(3c_1\right)}{6561a^3{x}^3}+\frac{512}{243}\cosh \left(3c_1\right)+\frac{{\sinh }^3\left(3c_1\right)}{34012224a^6{x}^6}+\frac{{\sinh }^2\left(3c_1\right)}{13122a^3{x}^3}+\frac{512}{243}\sinh \left(3c_1\right)}{4\sqrt{-\frac{64}{9}{a}^2{x}^2+\frac{\cosh \left(3c_1\right)}{81ax}+\frac{\sinh \left(3c_1\right)}{81ax}+\frac{\sqrt[3]{4529848320a^6\cosh \left(6c_1\right)x^6+4529848320a^6\sinh \left(6c_1\right)x^6+1105920a^3\cosh \left(9c_1\right)x^3+1105920a^3\sinh \left(9c_1\right)x^3+432\cosh \left(12c_1\right)+432\sinh \left(12c_1\right)+\sqrt{-3361919107433565782016a^{15}\cosh \left(9c_1\right)x^{15}-3361919107433565782016a^{15}\sinh \left(9c_1\right)x^{15}+8207810320882728960a^{12}\cosh \left(12c_1\right)x^{12}+8207810320882728960a^{12}\sinh \left(12c_1\right)x^{12}-5009649854054400a^9\cosh \left(15c_1\right)x^9-5009649854054400a^9\sinh \left(15c_1\right)x^9-978447237120a^6\cosh \left(18c_1\right)x^6-978447237120a^6\sinh \left(18c_1\right)x^6+955514880a^3\cosh \left(21c_1\right)x^3+955514880a^3\sinh \left(21c_1\right)x^3+186624\cosh \left(24c_1\right)+186624\sinh \left(24c_1\right)}}}{3888\sqrt[3]{2}{a}^2{x}^2}+\frac{16\sqrt[3]{2}(4096a^5\cosh \left(3c_1\right)x^5+4096a^5\sinh \left(3c_1\right)x^5+5a^2\cosh \left(6c_1\right)x^2+5a^2\sinh \left(6c_1\right)x^2)}{27a^2\sqrt[3]{4529848320a^6\cosh \left(6c_1\right)x^6+4529848320a^6\sinh \left(6c_1\right)x^6+1105920a^3\cosh \left(9c_1\right)x^3+1105920a^3\sinh \left(9c_1\right)x^3+432\cosh \left(12c_1\right)+432\sinh \left(12c_1\right)+\sqrt{-3361919107433565782016a^{15}\cosh \left(9c_1\right)x^{15}-3361919107433565782016a^{15}\sinh \left(9c_1\right)x^{15}+8207810320882728960a^{12}\cosh \left(12c_1\right)x^{12}+8207810320882728960a^{12}\sinh \left(12c_1\right)x^{12}-5009649854054400a^9\cosh \left(15c_1\right)x^9-5009649854054400a^9\sinh \left(15c_1\right)x^9-978447237120a^6\cosh \left(18c_1\right)x^6-978447237120a^6\sinh \left(18c_1\right)x^6+955514880a^3\cosh \left(21c_1\right)x^3+955514880a^3\sinh \left(21c_1\right)x^3+186624\cosh \left(24c_1\right)+186624\sinh \left(24c_1\right)}}{x}^2}+\frac{(1728a^3{x}^3-\cosh \left(3c_1\right)-\sinh \left(3c_1\right)){}^2}{419904a^4{x}^4}}}+\frac{2\cosh \left(3c_1\right)}{81ax}+\frac{2\sinh \left(3c_1\right)}{81ax}-\frac{\sqrt[3]{4529848320a^6\cosh \left(6c_1\right)x^6+4529848320a^6\sinh \left(6c_1\right)x^6+1105920a^3\cosh \left(9c_1\right)x^3+1105920a^3\sinh \left(9c_1\right)x^3+432\cosh \left(12c_1\right)+432\sinh \left(12c_1\right)+\sqrt{-3361919107433565782016a^{15}\cosh \left(9c_1\right)x^{15}-3361919107433565782016a^{15}\sinh \left(9c_1\right)x^{15}+8207810320882728960a^{12}\cosh \left(12c_1\right)x^{12}+8207810320882728960a^{12}\sinh \left(12c_1\right)x^{12}-5009649854054400a^9\cosh \left(15c_1\right)x^9-5009649854054400a^9\sinh \left(15c_1\right)x^9-978447237120a^6\cosh \left(18c_1\right)x^6-978447237120a^6\sinh \left(18c_1\right)x^6+955514880a^3\cosh \left(21c_1\right)x^3+955514880a^3\sinh \left(21c_1\right)x^3+186624\cosh \left(24c_1\right)+186624\sinh \left(24c_1\right)}}}{3888\sqrt[3]{2}{a}^2{x}^2}-\frac{16\sqrt[3]{2}(4096a^5\cosh \left(3c_1\right)x^5+4096a^5\sinh \left(3c_1\right)x^5+5a^2\cosh \left(6c_1\right)x^2+5a^2\sinh \left(6c_1\right)x^2)}{27a^2\sqrt[3]{4529848320a^6\cosh \left(6c_1\right)x^6+4529848320a^6\sinh \left(6c_1\right)x^6+1105920a^3\cosh \left(9c_1\right)x^3+1105920a^3\sinh \left(9c_1\right)x^3+432\cosh \left(12c_1\right)+432\sinh \left(12c_1\right)+\sqrt{-3361919107433565782016a^{15}\cosh \left(9c_1\right)x^{15}-3361919107433565782016a^{15}\sinh \left(9c_1\right)x^{15}+8207810320882728960a^{12}\cosh \left(12c_1\right)x^{12}+8207810320882728960a^{12}\sinh \left(12c_1\right)x^{12}-5009649854054400a^9\cosh \left(15c_1\right)x^9-5009649854054400a^9\sinh \left(15c_1\right)x^9-978447237120a^6\cosh \left(18c_1\right)x^6-978447237120a^6\sinh \left(18c_1\right)x^6+955514880a^3\cosh \left(21c_1\right)x^3+955514880a^3\sinh \left(21c_1\right)x^3+186624\cosh \left(24c_1\right)+186624\sinh \left(24c_1\right)}}{x}^2}+\frac{(1728a^3{x}^3-\cosh \left(3c_1\right)-\sinh \left(3c_1\right)){}^2}{209952a^4{x}^4}}+\frac{\cosh \left(3c_1\right)}{1296a^2{x}^2}+\frac{\sinh \left(3c_1\right)}{1296a^2{x}^2}}\}\}$$

Maple: cpu = 0.546 (sec), leaf count = 146 $$\{-x^2\mathit{\_}\mathit{C}\mathit{1}{\left(\frac{1}{x}(-y\left(x\right)+\sqrt{{\left(y\left(x\right)\right)}^2-4ax})\right)}^{\frac{3}{2}}{(-y\left(x\right)+\sqrt{{\left(y\left(x\right)\right)}^2-4ax})}^{-2}+x+\frac{4a{x}^2}{3}{(-y\left(x\right)+\sqrt{{\left(y\left(x\right)\right)}^2-4ax})}^{-2}=0,x^2\mathit{\_}\mathit{C}\mathit{1}{\left(\frac{1}{x}(-2y\left(x\right)-2\sqrt{{\left(y\left(x\right)\right)}^2-4ax})\right)}^{\frac{3}{2}}{(y\left(x\right)+\sqrt{{\left(y\left(x\right)\right)}^2-4ax})}^{-2}+x+\frac{4a{x}^2}{3}{(y\left(x\right)+\sqrt{{\left(y\left(x\right)\right)}^2-4ax})}^{-2}=0\}$$