2.419   ODE No. 419

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

$$x{y}^{\prime }(x{)}^2+2y(x)y^{\prime }(x)-x=0$$ ✓ Mathematica : cpu = 1.05168 (sec), leaf count = 9073

$$\{\{y(x)\to \frac{\cosh (3c_1)}{18x^2}+\frac{\sinh (3c_1)}{18x^2}-\frac{1}{2}\sqrt{\frac{4x^2}{9}+\frac{\sqrt[3]{2}\sqrt[3]{32x^{12}+40\cosh (6c_1)x^6+40\sinh (6c_1)x^6-\cosh (12c_1)-\sinh (12c_1)+\sqrt{4096\cosh (6c_1)x^{18}+4096\sinh (6c_1)x^{18}+768\cosh (12c_1)x^{12}+768\sinh (12c_1)x^{12}+48\cosh (18c_1)x^6+48\sinh (18c_1)x^6+\cosh (24c_1)+\sinh (24c_1)}}}{9x^2}+\frac{42^{2/3}(2x^8-\cosh (6c_1)x^2-\sinh (6c_1)x^2)}{9\sqrt[3]{32x^{12}+40\cosh (6c_1)x^6+40\sinh (6c_1)x^6-\cosh (12c_1)-\sinh (12c_1)+\sqrt{4096\cosh (6c_1)x^{18}+4096\sinh (6c_1)x^{18}+768\cosh (12c_1)x^{12}+768\sinh (12c_1)x^{12}+48\cosh (18c_1)x^6+48\sinh (18c_1)x^6+\cosh (24c_1)+\sinh (24c_1)}}{x}^2}+\frac{\cosh (6c_1)}{81x^4}+\frac{\sinh (6c_1)}{81x^4}}-\frac{1}{2}\sqrt{\frac{8x^2}{9}-\frac{-\frac{128}{27}\cosh (3c_1)+\frac{8\cosh (9c_1)}{729x^6}-\frac{128}{27}\sinh (3c_1)+\frac{8\sinh (9c_1)}{729x^6}}{4\sqrt{\frac{4x^2}{9}+\frac{\sqrt[3]{2}\sqrt[3]{32x^{12}+40\cosh (6c_1)x^6+40\sinh (6c_1)x^6-\cosh (12c_1)-\sinh (12c_1)+\sqrt{4096\cosh (6c_1)x^{18}+4096\sinh (6c_1)x^{18}+768\cosh (12c_1)x^{12}+768\sinh (12c_1)x^{12}+48\cosh (18c_1)x^6+48\sinh (18c_1)x^6+\cosh (24c_1)+\sinh (24c_1)}}}{9x^2}+\frac{42^{2/3}(2x^8-\cosh (6c_1)x^2-\sinh (6c_1)x^2)}{9\sqrt[3]{32x^{12}+40\cosh (6c_1)x^6+40\sinh (6c_1)x^6-\cosh (12c_1)-\sinh (12c_1)+\sqrt{4096\cosh (6c_1)x^{18}+4096\sinh (6c_1)x^{18}+768\cosh (12c_1)x^{12}+768\sinh (12c_1)x^{12}+48\cosh (18c_1)x^6+48\sinh (18c_1)x^6+\cosh (24c_1)+\sinh (24c_1)}}{x}^2}+\frac{\cosh (6c_1)}{81x^4}+\frac{\sinh (6c_1)}{81x^4}}}-\frac{\sqrt[3]{2}\sqrt[3]{32x^{12}+40\cosh (6c_1)x^6+40\sinh (6c_1)x^6-\cosh (12c_1)-\sinh (12c_1)+\sqrt{4096\cosh (6c_1)x^{18}+4096\sinh (6c_1)x^{18}+768\cosh (12c_1)x^{12}+768\sinh (12c_1)x^{12}+48\cosh (18c_1)x^6+48\sinh (18c_1)x^6+\cosh (24c_1)+\sinh (24c_1)}}}{9x^2}-\frac{42^{2/3}(2x^8-\cosh (6c_1)x^2-\sinh (6c_1)x^2)}{9\sqrt[3]{32x^{12}+40\cosh (6c_1)x^6+40\sinh (6c_1)x^6-\cosh (12c_1)-\sinh (12c_1)+\sqrt{4096\cosh (6c_1)x^{18}+4096\sinh (6c_1)x^{18}+768\cosh (12c_1)x^{12}+768\sinh (12c_1)x^{12}+48\cosh (18c_1)x^6+48\sinh (18c_1)x^6+\cosh (24c_1)+\sinh (24c_1)}}{x}^2}+\frac{2\cosh (6c_1)}{81x^4}+\frac{2\sinh (6c_1)}{81x^4}}\},\{y(x)\to \frac{\cosh (3c_1)}{18x^2}+\frac{\sinh (3c_1)}{18x^2}-\frac{1}{2}\sqrt{\frac{4x^2}{9}+\frac{\sqrt[3]{2}\sqrt[3]{32x^{12}+40\cosh (6c_1)x^6+40\sinh (6c_1)x^6-\cosh (12c_1)-\sinh (12c_1)+\sqrt{4096\cosh (6c_1)x^{18}+4096\sinh (6c_1)x^{18}+768\cosh (12c_1)x^{12}+768\sinh (12c_1)x^{12}+48\cosh (18c_1)x^6+48\sinh (18c_1)x^6+\cosh (24c_1)+\sinh (24c_1)}}}{9x^2}+\frac{42^{2/3}(2x^8-\cosh (6c_1)x^2-\sinh (6c_1)x^2)}{9\sqrt[3]{32x^{12}+40\cosh (6c_1)x^6+40\sinh (6c_1)x^6-\cosh (12c_1)-\sinh (12c_1)+\sqrt{4096\cosh (6c_1)x^{18}+4096\sinh (6c_1)x^{18}+768\cosh (12c_1)x^{12}+768\sinh (12c_1)x^{12}+48\cosh (18c_1)x^6+48\sinh (18c_1)x^6+\cosh (24c_1)+\sinh (24c_1)}}{x}^2}+\frac{\cosh (6c_1)}{81x^4}+\frac{\sinh (6c_1)}{81x^4}}+\frac{1}{2}\sqrt{\frac{8x^2}{9}-\frac{-\frac{128}{27}\cosh (3c_1)+\frac{8\cosh (9c_1)}{729x^6}-\frac{128}{27}\sinh (3c_1)+\frac{8\sinh (9c_1)}{729x^6}}{4\sqrt{\frac{4x^2}{9}+\frac{\sqrt[3]{2}\sqrt[3]{32x^{12}+40\cosh (6c_1)x^6+40\sinh (6c_1)x^6-\cosh (12c_1)-\sinh (12c_1)+\sqrt{4096\cosh (6c_1)x^{18}+4096\sinh (6c_1)x^{18}+768\cosh (12c_1)x^{12}+768\sinh (12c_1)x^{12}+48\cosh (18c_1)x^6+48\sinh (18c_1)x^6+\cosh (24c_1)+\sinh (24c_1)}}}{9x^2}+\frac{42^{2/3}(2x^8-\cosh (6c_1)x^2-\sinh (6c_1)x^2)}{9\sqrt[3]{32x^{12}+40\cosh (6c_1)x^6+40\sinh (6c_1)x^6-\cosh (12c_1)-\sinh (12c_1)+\sqrt{4096\cosh (6c_1)x^{18}+4096\sinh (6c_1)x^{18}+768\cosh (12c_1)x^{12}+768\sinh (12c_1)x^{12}+48\cosh (18c_1)x^6+48\sinh (18c_1)x^6+\cosh (24c_1)+\sinh (24c_1)}}{x}^2}+\frac{\cosh (6c_1)}{81x^4}+\frac{\sinh (6c_1)}{81x^4}}}-\frac{\sqrt[3]{2}\sqrt[3]{32x^{12}+40\cosh (6c_1)x^6+40\sinh (6c_1)x^6-\cosh (12c_1)-\sinh (12c_1)+\sqrt{4096\cosh (6c_1)x^{18}+4096\sinh (6c_1)x^{18}+768\cosh (12c_1)x^{12}+768\sinh (12c_1)x^{12}+48\cosh (18c_1)x^6+48\sinh (18c_1)x^6+\cosh (24c_1)+\sinh (24c_1)}}}{9x^2}-\frac{42^{2/3}(2x^8-\cosh (6c_1)x^2-\sinh (6c_1)x^2)}{9\sqrt[3]{32x^{12}+40\cosh (6c_1)x^6+40\sinh (6c_1)x^6-\cosh (12c_1)-\sinh (12c_1)+\sqrt{4096\cosh (6c_1)x^{18}+4096\sinh (6c_1)x^{18}+768\cosh (12c_1)x^{12}+768\sinh (12c_1)x^{12}+48\cosh (18c_1)x^6+48\sinh (18c_1)x^6+\cosh (24c_1)+\sinh (24c_1)}}{x}^2}+\frac{2\cosh (6c_1)}{81x^4}+\frac{2\sinh (6c_1)}{81x^4}}\},\{y(x)\to \frac{\cosh (3c_1)}{18x^2}+\frac{\sinh (3c_1)}{18x^2}+\frac{1}{2}\sqrt{\frac{4x^2}{9}+\frac{\sqrt[3]{2}\sqrt[3]{32x^{12}+40\cosh (6c_1)x^6+40\sinh (6c_1)x^6-\cosh (12c_1)-\sinh (12c_1)+\sqrt{4096\cosh (6c_1)x^{18}+4096\sinh (6c_1)x^{18}+768\cosh (12c_1)x^{12}+768\sinh (12c_1)x^{12}+48\cosh (18c_1)x^6+48\sinh (18c_1)x^6+\cosh (24c_1)+\sinh (24c_1)}}}{9x^2}+\frac{42^{2/3}(2x^8-\cosh (6c_1)x^2-\sinh (6c_1)x^2)}{9\sqrt[3]{32x^{12}+40\cosh (6c_1)x^6+40\sinh (6c_1)x^6-\cosh (12c_1)-\sinh (12c_1)+\sqrt{4096\cosh (6c_1)x^{18}+4096\sinh (6c_1)x^{18}+768\cosh (12c_1)x^{12}+768\sinh (12c_1)x^{12}+48\cosh (18c_1)x^6+48\sinh (18c_1)x^6+\cosh (24c_1)+\sinh (24c_1)}}{x}^2}+\frac{\cosh (6c_1)}{81x^4}+\frac{\sinh (6c_1)}{81x^4}}-\frac{1}{2}\sqrt{\frac{8x^2}{9}+\frac{-\frac{128}{27}\cosh (3c_1)+\frac{8\cosh (9c_1)}{729x^6}-\frac{128}{27}\sinh (3c_1)+\frac{8\sinh (9c_1)}{729x^6}}{4\sqrt{\frac{4x^2}{9}+\frac{\sqrt[3]{2}\sqrt[3]{32x^{12}+40\cosh (6c_1)x^6+40\sinh (6c_1)x^6-\cosh (12c_1)-\sinh (12c_1)+\sqrt{4096\cosh (6c_1)x^{18}+4096\sinh (6c_1)x^{18}+768\cosh (12c_1)x^{12}+768\sinh (12c_1)x^{12}+48\cosh (18c_1)x^6+48\sinh (18c_1)x^6+\cosh (24c_1)+\sinh (24c_1)}}}{9x^2}+\frac{42^{2/3}(2x^8-\cosh (6c_1)x^2-\sinh (6c_1)x^2)}{9\sqrt[3]{32x^{12}+40\cosh (6c_1)x^6+40\sinh (6c_1)x^6-\cosh (12c_1)-\sinh (12c_1)+\sqrt{4096\cosh (6c_1)x^{18}+4096\sinh (6c_1)x^{18}+768\cosh (12c_1)x^{12}+768\sinh (12c_1)x^{12}+48\cosh (18c_1)x^6+48\sinh (18c_1)x^6+\cosh (24c_1)+\sinh (24c_1)}}{x}^2}+\frac{\cosh (6c_1)}{81x^4}+\frac{\sinh (6c_1)}{81x^4}}}-\frac{\sqrt[3]{2}\sqrt[3]{32x^{12}+40\cosh (6c_1)x^6+40\sinh (6c_1)x^6-\cosh (12c_1)-\sinh (12c_1)+\sqrt{4096\cosh (6c_1)x^{18}+4096\sinh (6c_1)x^{18}+768\cosh (12c_1)x^{12}+768\sinh (12c_1)x^{12}+48\cosh (18c_1)x^6+48\sinh (18c_1)x^6+\cosh (24c_1)+\sinh (24c_1)}}}{9x^2}-\frac{42^{2/3}(2x^8-\cosh (6c_1)x^2-\sinh (6c_1)x^2)}{9\sqrt[3]{32x^{12}+40\cosh (6c_1)x^6+40\sinh (6c_1)x^6-\cosh (12c_1)-\sinh (12c_1)+\sqrt{4096\cosh (6c_1)x^{18}+4096\sinh (6c_1)x^{18}+768\cosh (12c_1)x^{12}+768\sinh (12c_1)x^{12}+48\cosh (18c_1)x^6+48\sinh (18c_1)x^6+\cosh (24c_1)+\sinh (24c_1)}}{x}^2}+\frac{2\cosh (6c_1)}{81x^4}+\frac{2\sinh (6c_1)}{81x^4}}\},\{y(x)\to \frac{\cosh (3c_1)}{18x^2}+\frac{\sinh (3c_1)}{18x^2}+\frac{1}{2}\sqrt{\frac{4x^2}{9}+\frac{\sqrt[3]{2}\sqrt[3]{32x^{12}+40\cosh (6c_1)x^6+40\sinh (6c_1)x^6-\cosh (12c_1)-\sinh (12c_1)+\sqrt{4096\cosh (6c_1)x^{18}+4096\sinh (6c_1)x^{18}+768\cosh (12c_1)x^{12}+768\sinh (12c_1)x^{12}+48\cosh (18c_1)x^6+48\sinh (18c_1)x^6+\cosh (24c_1)+\sinh (24c_1)}}}{9x^2}+\frac{42^{2/3}(2x^8-\cosh (6c_1)x^2-\sinh (6c_1)x^2)}{9\sqrt[3]{32x^{12}+40\cosh (6c_1)x^6+40\sinh (6c_1)x^6-\cosh (12c_1)-\sinh (12c_1)+\sqrt{4096\cosh (6c_1)x^{18}+4096\sinh (6c_1)x^{18}+768\cosh (12c_1)x^{12}+768\sinh (12c_1)x^{12}+48\cosh (18c_1)x^6+48\sinh (18c_1)x^6+\cosh (24c_1)+\sinh (24c_1)}}{x}^2}+\frac{\cosh (6c_1)}{81x^4}+\frac{\sinh (6c_1)}{81x^4}}+\frac{1}{2}\sqrt{\frac{8x^2}{9}+\frac{-\frac{128}{27}\cosh (3c_1)+\frac{8\cosh (9c_1)}{729x^6}-\frac{128}{27}\sinh (3c_1)+\frac{8\sinh (9c_1)}{729x^6}}{4\sqrt{\frac{4x^2}{9}+\frac{\sqrt[3]{2}\sqrt[3]{32x^{12}+40\cosh (6c_1)x^6+40\sinh (6c_1)x^6-\cosh (12c_1)-\sinh (12c_1)+\sqrt{4096\cosh (6c_1)x^{18}+4096\sinh (6c_1)x^{18}+768\cosh (12c_1)x^{12}+768\sinh (12c_1)x^{12}+48\cosh (18c_1)x^6+48\sinh (18c_1)x^6+\cosh (24c_1)+\sinh (24c_1)}}}{9x^2}+\frac{42^{2/3}(2x^8-\cosh (6c_1)x^2-\sinh (6c_1)x^2)}{9\sqrt[3]{32x^{12}+40\cosh (6c_1)x^6+40\sinh (6c_1)x^6-\cosh (12c_1)-\sinh (12c_1)+\sqrt{4096\cosh (6c_1)x^{18}+4096\sinh (6c_1)x^{18}+768\cosh (12c_1)x^{12}+768\sinh (12c_1)x^{12}+48\cosh (18c_1)x^6+48\sinh (18c_1)x^6+\cosh (24c_1)+\sinh (24c_1)}}{x}^2}+\frac{\cosh (6c_1)}{81x^4}+\frac{\sinh (6c_1)}{81x^4}}}-\frac{\sqrt[3]{2}\sqrt[3]{32x^{12}+40\cosh (6c_1)x^6+40\sinh (6c_1)x^6-\cosh (12c_1)-\sinh (12c_1)+\sqrt{4096\cosh (6c_1)x^{18}+4096\sinh (6c_1)x^{18}+768\cosh (12c_1)x^{12}+768\sinh (12c_1)x^{12}+48\cosh (18c_1)x^6+48\sinh (18c_1)x^6+\cosh (24c_1)+\sinh (24c_1)}}}{9x^2}-\frac{42^{2/3}(2x^8-\cosh (6c_1)x^2-\sinh (6c_1)x^2)}{9\sqrt[3]{32x^{12}+40\cosh (6c_1)x^6+40\sinh (6c_1)x^6-\cosh (12c_1)-\sinh (12c_1)+\sqrt{4096\cosh (6c_1)x^{18}+4096\sinh (6c_1)x^{18}+768\cosh (12c_1)x^{12}+768\sinh (12c_1)x^{12}+48\cosh (18c_1)x^6+48\sinh (18c_1)x^6+\cosh (24c_1)+\sinh (24c_1)}}{x}^2}+\frac{2\cosh (6c_1)}{81x^4}+\frac{2\sinh (6c_1)}{81x^4}}\},\{y(x)\to -\frac{\cosh (3c_1)}{18x^2}+\frac{\sinh (3c_1)}{18x^2}-\frac{1}{2}\sqrt{\frac{4x^2}{9}+\frac{\sqrt[3]{2}\sqrt[3]{32x^{12}+40\cosh (6c_1)x^6-40\sinh (6c_1)x^6-\cosh (12c_1)+\sinh (12c_1)+(\cosh (18c_1)-\sinh (18c_1))\sqrt{4096\cosh (30c_1)x^{18}+4096\sinh (30c_1)x^{18}+768\cosh (24c_1)x^{12}+768\sinh (24c_1)x^{12}+48\cosh (18c_1)x^6+48\sinh (18c_1)x^6+\cosh (12c_1)+\sinh (12c_1)}}}{9x^2}+\frac{42^{2/3}(\cosh (12c_1)-\sinh (12c_1))(2\cosh (12c_1)x^8+2\sinh (12c_1)x^8-\cosh (6c_1)x^2-\sinh (6c_1)x^2)}{9\sqrt[3]{32x^{12}+40\cosh (6c_1)x^6-40\sinh (6c_1)x^6-\cosh (12c_1)+\sinh (12c_1)+(\cosh (18c_1)-\sinh (18c_1))\sqrt{4096\cosh (30c_1)x^{18}+4096\sinh (30c_1)x^{18}+768\cosh (24c_1)x^{12}+768\sinh (24c_1)x^{12}+48\cosh (18c_1)x^6+48\sinh (18c_1)x^6+\cosh (12c_1)+\sinh (12c_1)}}{x}^2}+\frac{\cosh (6c_1)}{81x^4}-\frac{\sinh (6c_1)}{81x^4}}-\frac{1}{2}\sqrt{\frac{8x^2}{9}-\frac{\frac{128}{27}\cosh (3c_1)-\frac{8\cosh (9c_1)}{729x^6}-\frac{128}{27}\sinh (3c_1)+\frac{8\sinh (9c_1)}{729x^6}}{4\sqrt{\frac{4x^2}{9}+\frac{\sqrt[3]{2}\sqrt[3]{32x^{12}+40\cosh (6c_1)x^6-40\sinh (6c_1)x^6-\cosh (12c_1)+\sinh (12c_1)+(\cosh (18c_1)-\sinh (18c_1))\sqrt{4096\cosh (30c_1)x^{18}+4096\sinh (30c_1)x^{18}+768\cosh (24c_1)x^{12}+768\sinh (24c_1)x^{12}+48\cosh (18c_1)x^6+48\sinh (18c_1)x^6+\cosh (12c_1)+\sinh (12c_1)}}}{9x^2}+\frac{42^{2/3}(\cosh (12c_1)-\sinh (12c_1))(2\cosh (12c_1)x^8+2\sinh (12c_1)x^8-\cosh (6c_1)x^2-\sinh (6c_1)x^2)}{9\sqrt[3]{32x^{12}+40\cosh (6c_1)x^6-40\sinh (6c_1)x^6-\cosh (12c_1)+\sinh (12c_1)+(\cosh (18c_1)-\sinh (18c_1))\sqrt{4096\cosh (30c_1)x^{18}+4096\sinh (30c_1)x^{18}+768\cosh (24c_1)x^{12}+768\sinh (24c_1)x^{12}+48\cosh (18c_1)x^6+48\sinh (18c_1)x^6+\cosh (12c_1)+\sinh (12c_1)}}{x}^2}+\frac{\cosh (6c_1)}{81x^4}-\frac{\sinh (6c_1)}{81x^4}}}-\frac{\sqrt[3]{2}\sqrt[3]{32x^{12}+40\cosh (6c_1)x^6-40\sinh (6c_1)x^6-\cosh (12c_1)+\sinh (12c_1)+(\cosh (18c_1)-\sinh (18c_1))\sqrt{4096\cosh (30c_1)x^{18}+4096\sinh (30c_1)x^{18}+768\cosh (24c_1)x^{12}+768\sinh (24c_1)x^{12}+48\cosh (18c_1)x^6+48\sinh (18c_1)x^6+\cosh (12c_1)+\sinh (12c_1)}}}{9x^2}-\frac{42^{2/3}(\cosh (12c_1)-\sinh (12c_1))(2\cosh (12c_1)x^8+2\sinh (12c_1)x^8-\cosh (6c_1)x^2-\sinh (6c_1)x^2)}{9\sqrt[3]{32x^{12}+40\cosh (6c_1)x^6-40\sinh (6c_1)x^6-\cosh (12c_1)+\sinh (12c_1)+(\cosh (18c_1)-\sinh (18c_1))\sqrt{4096\cosh (30c_1)x^{18}+4096\sinh (30c_1)x^{18}+768\cosh (24c_1)x^{12}+768\sinh (24c_1)x^{12}+48\cosh (18c_1)x^6+48\sinh (18c_1)x^6+\cosh (12c_1)+\sinh (12c_1)}}{x}^2}+\frac{2\cosh (6c_1)}{81x^4}-\frac{2\sinh (6c_1)}{81x^4}}\},\{y(x)\to -\frac{\cosh (3c_1)}{18x^2}+\frac{\sinh (3c_1)}{18x^2}-\frac{1}{2}\sqrt{\frac{4x^2}{9}+\frac{\sqrt[3]{2}\sqrt[3]{32x^{12}+40\cosh (6c_1)x^6-40\sinh (6c_1)x^6-\cosh (12c_1)+\sinh (12c_1)+(\cosh (18c_1)-\sinh (18c_1))\sqrt{4096\cosh (30c_1)x^{18}+4096\sinh (30c_1)x^{18}+768\cosh (24c_1)x^{12}+768\sinh (24c_1)x^{12}+48\cosh (18c_1)x^6+48\sinh (18c_1)x^6+\cosh (12c_1)+\sinh (12c_1)}}}{9x^2}+\frac{42^{2/3}(\cosh (12c_1)-\sinh (12c_1))(2\cosh (12c_1)x^8+2\sinh (12c_1)x^8-\cosh (6c_1)x^2-\sinh (6c_1)x^2)}{9\sqrt[3]{32x^{12}+40\cosh (6c_1)x^6-40\sinh (6c_1)x^6-\cosh (12c_1)+\sinh (12c_1)+(\cosh (18c_1)-\sinh (18c_1))\sqrt{4096\cosh (30c_1)x^{18}+4096\sinh (30c_1)x^{18}+768\cosh (24c_1)x^{12}+768\sinh (24c_1)x^{12}+48\cosh (18c_1)x^6+48\sinh (18c_1)x^6+\cosh (12c_1)+\sinh (12c_1)}}{x}^2}+\frac{\cosh (6c_1)}{81x^4}-\frac{\sinh (6c_1)}{81x^4}}+\frac{1}{2}\sqrt{\frac{8x^2}{9}-\frac{\frac{128}{27}\cosh (3c_1)-\frac{8\cosh (9c_1)}{729x^6}-\frac{128}{27}\sinh (3c_1)+\frac{8\sinh (9c_1)}{729x^6}}{4\sqrt{\frac{4x^2}{9}+\frac{\sqrt[3]{2}\sqrt[3]{32x^{12}+40\cosh (6c_1)x^6-40\sinh (6c_1)x^6-\cosh (12c_1)+\sinh (12c_1)+(\cosh (18c_1)-\sinh (18c_1))\sqrt{4096\cosh (30c_1)x^{18}+4096\sinh (30c_1)x^{18}+768\cosh (24c_1)x^{12}+768\sinh (24c_1)x^{12}+48\cosh (18c_1)x^6+48\sinh (18c_1)x^6+\cosh (12c_1)+\sinh (12c_1)}}}{9x^2}+\frac{42^{2/3}(\cosh (12c_1)-\sinh (12c_1))(2\cosh (12c_1)x^8+2\sinh (12c_1)x^8-\cosh (6c_1)x^2-\sinh (6c_1)x^2)}{9\sqrt[3]{32x^{12}+40\cosh (6c_1)x^6-40\sinh (6c_1)x^6-\cosh (12c_1)+\sinh (12c_1)+(\cosh (18c_1)-\sinh (18c_1))\sqrt{4096\cosh (30c_1)x^{18}+4096\sinh (30c_1)x^{18}+768\cosh (24c_1)x^{12}+768\sinh (24c_1)x^{12}+48\cosh (18c_1)x^6+48\sinh (18c_1)x^6+\cosh (12c_1)+\sinh (12c_1)}}{x}^2}+\frac{\cosh (6c_1)}{81x^4}-\frac{\sinh (6c_1)}{81x^4}}}-\frac{\sqrt[3]{2}\sqrt[3]{32x^{12}+40\cosh (6c_1)x^6-40\sinh (6c_1)x^6-\cosh (12c_1)+\sinh (12c_1)+(\cosh (18c_1)-\sinh (18c_1))\sqrt{4096\cosh (30c_1)x^{18}+4096\sinh (30c_1)x^{18}+768\cosh (24c_1)x^{12}+768\sinh (24c_1)x^{12}+48\cosh (18c_1)x^6+48\sinh (18c_1)x^6+\cosh (12c_1)+\sinh (12c_1)}}}{9x^2}-\frac{42^{2/3}(\cosh (12c_1)-\sinh (12c_1))(2\cosh (12c_1)x^8+2\sinh (12c_1)x^8-\cosh (6c_1)x^2-\sinh (6c_1)x^2)}{9\sqrt[3]{32x^{12}+40\cosh (6c_1)x^6-40\sinh (6c_1)x^6-\cosh (12c_1)+\sinh (12c_1)+(\cosh (18c_1)-\sinh (18c_1))\sqrt{4096\cosh (30c_1)x^{18}+4096\sinh (30c_1)x^{18}+768\cosh (24c_1)x^{12}+768\sinh (24c_1)x^{12}+48\cosh (18c_1)x^6+48\sinh (18c_1)x^6+\cosh (12c_1)+\sinh (12c_1)}}{x}^2}+\frac{2\cosh (6c_1)}{81x^4}-\frac{2\sinh (6c_1)}{81x^4}}\},\{y(x)\to -\frac{\cosh (3c_1)}{18x^2}+\frac{\sinh (3c_1)}{18x^2}+\frac{1}{2}\sqrt{\frac{4x^2}{9}+\frac{\sqrt[3]{2}\sqrt[3]{32x^{12}+40\cosh (6c_1)x^6-40\sinh (6c_1)x^6-\cosh (12c_1)+\sinh (12c_1)+(\cosh (18c_1)-\sinh (18c_1))\sqrt{4096\cosh (30c_1)x^{18}+4096\sinh (30c_1)x^{18}+768\cosh (24c_1)x^{12}+768\sinh (24c_1)x^{12}+48\cosh (18c_1)x^6+48\sinh (18c_1)x^6+\cosh (12c_1)+\sinh (12c_1)}}}{9x^2}+\frac{42^{2/3}(\cosh (12c_1)-\sinh (12c_1))(2\cosh (12c_1)x^8+2\sinh (12c_1)x^8-\cosh (6c_1)x^2-\sinh (6c_1)x^2)}{9\sqrt[3]{32x^{12}+40\cosh (6c_1)x^6-40\sinh (6c_1)x^6-\cosh (12c_1)+\sinh (12c_1)+(\cosh (18c_1)-\sinh (18c_1))\sqrt{4096\cosh (30c_1)x^{18}+4096\sinh (30c_1)x^{18}+768\cosh (24c_1)x^{12}+768\sinh (24c_1)x^{12}+48\cosh (18c_1)x^6+48\sinh (18c_1)x^6+\cosh (12c_1)+\sinh (12c_1)}}{x}^2}+\frac{\cosh (6c_1)}{81x^4}-\frac{\sinh (6c_1)}{81x^4}}-\frac{1}{2}\sqrt{\frac{8x^2}{9}+\frac{\frac{128}{27}\cosh (3c_1)-\frac{8\cosh (9c_1)}{729x^6}-\frac{128}{27}\sinh (3c_1)+\frac{8\sinh (9c_1)}{729x^6}}{4\sqrt{\frac{4x^2}{9}+\frac{\sqrt[3]{2}\sqrt[3]{32x^{12}+40\cosh (6c_1)x^6-40\sinh (6c_1)x^6-\cosh (12c_1)+\sinh (12c_1)+(\cosh (18c_1)-\sinh (18c_1))\sqrt{4096\cosh (30c_1)x^{18}+4096\sinh (30c_1)x^{18}+768\cosh (24c_1)x^{12}+768\sinh (24c_1)x^{12}+48\cosh (18c_1)x^6+48\sinh (18c_1)x^6+\cosh (12c_1)+\sinh (12c_1)}}}{9x^2}+\frac{42^{2/3}(\cosh (12c_1)-\sinh (12c_1))(2\cosh (12c_1)x^8+2\sinh (12c_1)x^8-\cosh (6c_1)x^2-\sinh (6c_1)x^2)}{9\sqrt[3]{32x^{12}+40\cosh (6c_1)x^6-40\sinh (6c_1)x^6-\cosh (12c_1)+\sinh (12c_1)+(\cosh (18c_1)-\sinh (18c_1))\sqrt{4096\cosh (30c_1)x^{18}+4096\sinh (30c_1)x^{18}+768\cosh (24c_1)x^{12}+768\sinh (24c_1)x^{12}+48\cosh (18c_1)x^6+48\sinh (18c_1)x^6+\cosh (12c_1)+\sinh (12c_1)}}{x}^2}+\frac{\cosh (6c_1)}{81x^4}-\frac{\sinh (6c_1)}{81x^4}}}-\frac{\sqrt[3]{2}\sqrt[3]{32x^{12}+40\cosh (6c_1)x^6-40\sinh (6c_1)x^6-\cosh (12c_1)+\sinh (12c_1)+(\cosh (18c_1)-\sinh (18c_1))\sqrt{4096\cosh (30c_1)x^{18}+4096\sinh (30c_1)x^{18}+768\cosh (24c_1)x^{12}+768\sinh (24c_1)x^{12}+48\cosh (18c_1)x^6+48\sinh (18c_1)x^6+\cosh (12c_1)+\sinh (12c_1)}}}{9x^2}-\frac{42^{2/3}(\cosh (12c_1)-\sinh (12c_1))(2\cosh (12c_1)x^8+2\sinh (12c_1)x^8-\cosh (6c_1)x^2-\sinh (6c_1)x^2)}{9\sqrt[3]{32x^{12}+40\cosh (6c_1)x^6-40\sinh (6c_1)x^6-\cosh (12c_1)+\sinh (12c_1)+(\cosh (18c_1)-\sinh (18c_1))\sqrt{4096\cosh (30c_1)x^{18}+4096\sinh (30c_1)x^{18}+768\cosh (24c_1)x^{12}+768\sinh (24c_1)x^{12}+48\cosh (18c_1)x^6+48\sinh (18c_1)x^6+\cosh (12c_1)+\sinh (12c_1)}}{x}^2}+\frac{2\cosh (6c_1)}{81x^4}-\frac{2\sinh (6c_1)}{81x^4}}\},\{y(x)\to -\frac{\cosh (3c_1)}{18x^2}+\frac{\sinh (3c_1)}{18x^2}+\frac{1}{2}\sqrt{\frac{4x^2}{9}+\frac{\sqrt[3]{2}\sqrt[3]{32x^{12}+40\cosh (6c_1)x^6-40\sinh (6c_1)x^6-\cosh (12c_1)+\sinh (12c_1)+(\cosh (18c_1)-\sinh (18c_1))\sqrt{4096\cosh (30c_1)x^{18}+4096\sinh (30c_1)x^{18}+768\cosh (24c_1)x^{12}+768\sinh (24c_1)x^{12}+48\cosh (18c_1)x^6+48\sinh (18c_1)x^6+\cosh (12c_1)+\sinh (12c_1)}}}{9x^2}+\frac{42^{2/3}(\cosh (12c_1)-\sinh (12c_1))(2\cosh (12c_1)x^8+2\sinh (12c_1)x^8-\cosh (6c_1)x^2-\sinh (6c_1)x^2)}{9\sqrt[3]{32x^{12}+40\cosh (6c_1)x^6-40\sinh (6c_1)x^6-\cosh (12c_1)+\sinh (12c_1)+(\cosh (18c_1)-\sinh (18c_1))\sqrt{4096\cosh (30c_1)x^{18}+4096\sinh (30c_1)x^{18}+768\cosh (24c_1)x^{12}+768\sinh (24c_1)x^{12}+48\cosh (18c_1)x^6+48\sinh (18c_1)x^6+\cosh (12c_1)+\sinh (12c_1)}}{x}^2}+\frac{\cosh (6c_1)}{81x^4}-\frac{\sinh (6c_1)}{81x^4}}+\frac{1}{2}\sqrt{\frac{8x^2}{9}+\frac{\frac{128}{27}\cosh (3c_1)-\frac{8\cosh (9c_1)}{729x^6}-\frac{128}{27}\sinh (3c_1)+\frac{8\sinh (9c_1)}{729x^6}}{4\sqrt{\frac{4x^2}{9}+\frac{\sqrt[3]{2}\sqrt[3]{32x^{12}+40\cosh (6c_1)x^6-40\sinh (6c_1)x^6-\cosh (12c_1)+\sinh (12c_1)+(\cosh (18c_1)-\sinh (18c_1))\sqrt{4096\cosh (30c_1)x^{18}+4096\sinh (30c_1)x^{18}+768\cosh (24c_1)x^{12}+768\sinh (24c_1)x^{12}+48\cosh (18c_1)x^6+48\sinh (18c_1)x^6+\cosh (12c_1)+\sinh (12c_1)}}}{9x^2}+\frac{42^{2/3}(\cosh (12c_1)-\sinh (12c_1))(2\cosh (12c_1)x^8+2\sinh (12c_1)x^8-\cosh (6c_1)x^2-\sinh (6c_1)x^2)}{9\sqrt[3]{32x^{12}+40\cosh (6c_1)x^6-40\sinh (6c_1)x^6-\cosh (12c_1)+\sinh (12c_1)+(\cosh (18c_1)-\sinh (18c_1))\sqrt{4096\cosh (30c_1)x^{18}+4096\sinh (30c_1)x^{18}+768\cosh (24c_1)x^{12}+768\sinh (24c_1)x^{12}+48\cosh (18c_1)x^6+48\sinh (18c_1)x^6+\cosh (12c_1)+\sinh (12c_1)}}{x}^2}+\frac{\cosh (6c_1)}{81x^4}-\frac{\sinh (6c_1)}{81x^4}}}-\frac{\sqrt[3]{2}\sqrt[3]{32x^{12}+40\cosh (6c_1)x^6-40\sinh (6c_1)x^6-\cosh (12c_1)+\sinh (12c_1)+(\cosh (18c_1)-\sinh (18c_1))\sqrt{4096\cosh (30c_1)x^{18}+4096\sinh (30c_1)x^{18}+768\cosh (24c_1)x^{12}+768\sinh (24c_1)x^{12}+48\cosh (18c_1)x^6+48\sinh (18c_1)x^6+\cosh (12c_1)+\sinh (12c_1)}}}{9x^2}-\frac{42^{2/3}(\cosh (12c_1)-\sinh (12c_1))(2\cosh (12c_1)x^8+2\sinh (12c_1)x^8-\cosh (6c_1)x^2-\sinh (6c_1)x^2)}{9\sqrt[3]{32x^{12}+40\cosh (6c_1)x^6-40\sinh (6c_1)x^6-\cosh (12c_1)+\sinh (12c_1)+(\cosh (18c_1)-\sinh (18c_1))\sqrt{4096\cosh (30c_1)x^{18}+4096\sinh (30c_1)x^{18}+768\cosh (24c_1)x^{12}+768\sinh (24c_1)x^{12}+48\cosh (18c_1)x^6+48\sinh (18c_1)x^6+\cosh (12c_1)+\sinh (12c_1)}}{x}^2}+\frac{2\cosh (6c_1)}{81x^4}-\frac{2\sinh (6c_1)}{81x^4}}\}\}$$ ✓ Maple : cpu = 0.059 (sec), leaf count = 109

$$\{x+\frac{\mathit{\_}\mathit{C}\mathit{1}}{x}(y\left(x\right)-\sqrt{{\left(y\left(x\right)\right)}^2+x^2}){\left(\frac{1}{x^2}(2x^2+6{\left(y\left(x\right)\right)}^2-6y\left(x\right)\sqrt{{\left(y\left(x\right)\right)}^2+x^2})\right)}^{-\frac{2}{3}}=0,\frac{\mathit{\_}\mathit{C}\mathit{1}}{x}(\sqrt{{\left(y\left(x\right)\right)}^2+x^2}+y\left(x\right)){\left(\frac{1}{x^2}(3y\left(x\right)\sqrt{{\left(y\left(x\right)\right)}^2+x^2}+x^2+3{\left(y\left(x\right)\right)}^2)\right)}^{-\frac{2}{3}}+x=0\}$$