2.380   ODE No. 380

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

$${\text{Global}\stackrel{`}{}\text{y}}^{\prime }(\text{Global}\stackrel{`}{}\text{x}{)}^2+2\text{Global}\stackrel{`}{}\text{x}{\text{Global}\stackrel{`}{}\text{y}}^{\prime }(\text{Global}\stackrel{`}{}\text{x})-\text{Global}\stackrel{`}{}\text{y}(\text{Global}\stackrel{`}{}\text{x})=0$$ ✓ Mathematica : cpu = 0.427229 (sec), leaf count = 1757

$$\{\{\text{Global}\stackrel{`}{}\text{y}(\text{Global}\stackrel{`}{}\text{x})\to -\frac{{\text{Global}\stackrel{`}{}\text{x}}^2}{4}-\frac{1}{4}\sqrt[3]{{\text{Global}\stackrel{`}{}\text{x}}^6-20\cosh \left(3c_1\right){\text{Global}\stackrel{`}{}\text{x}}^3-20\sinh \left(3c_1\right){\text{Global}\stackrel{`}{}\text{x}}^3-8\cosh \left(6c_1\right)-8\sinh \left(6c_1\right)+8\sqrt{-\cosh \left(3c_1\right){\text{Global}\stackrel{`}{}\text{x}}^9-\sinh \left(3c_1\right){\text{Global}\stackrel{`}{}\text{x}}^9+3\cosh \left(6c_1\right){\text{Global}\stackrel{`}{}\text{x}}^6+3\sinh \left(6c_1\right){\text{Global}\stackrel{`}{}\text{x}}^6-3\cosh \left(9c_1\right){\text{Global}\stackrel{`}{}\text{x}}^3-3\sinh \left(9c_1\right){\text{Global}\stackrel{`}{}\text{x}}^3+\cosh \left(12c_1\right)+\sinh \left(12c_1\right)}}+\frac{-9{\text{Global}\stackrel{`}{}\text{x}}^4-72\cosh \left(3c_1\right)\text{Global}\stackrel{`}{}\text{x}-72\sinh \left(3c_1\right)\text{Global}\stackrel{`}{}\text{x}}{36\sqrt[3]{{\text{Global}\stackrel{`}{}\text{x}}^6-20\cosh \left(3c_1\right){\text{Global}\stackrel{`}{}\text{x}}^3-20\sinh \left(3c_1\right){\text{Global}\stackrel{`}{}\text{x}}^3-8\cosh \left(6c_1\right)-8\sinh \left(6c_1\right)+8\sqrt{-\cosh \left(3c_1\right){\text{Global}\stackrel{`}{}\text{x}}^9-\sinh \left(3c_1\right){\text{Global}\stackrel{`}{}\text{x}}^9+3\cosh \left(6c_1\right){\text{Global}\stackrel{`}{}\text{x}}^6+3\sinh \left(6c_1\right){\text{Global}\stackrel{`}{}\text{x}}^6-3\cosh \left(9c_1\right){\text{Global}\stackrel{`}{}\text{x}}^3-3\sinh \left(9c_1\right){\text{Global}\stackrel{`}{}\text{x}}^3+\cosh \left(12c_1\right)+\sinh \left(12c_1\right)}}}\},\{\text{Global}\stackrel{`}{}\text{y}(\text{Global}\stackrel{`}{}\text{x})\to -\frac{{\text{Global}\stackrel{`}{}\text{x}}^2}{4}+\frac{1}{8}(1-i\sqrt{3})\sqrt[3]{{\text{Global}\stackrel{`}{}\text{x}}^6-20\cosh \left(3c_1\right){\text{Global}\stackrel{`}{}\text{x}}^3-20\sinh \left(3c_1\right){\text{Global}\stackrel{`}{}\text{x}}^3-8\cosh \left(6c_1\right)-8\sinh \left(6c_1\right)+8\sqrt{-\cosh \left(3c_1\right){\text{Global}\stackrel{`}{}\text{x}}^9-\sinh \left(3c_1\right){\text{Global}\stackrel{`}{}\text{x}}^9+3\cosh \left(6c_1\right){\text{Global}\stackrel{`}{}\text{x}}^6+3\sinh \left(6c_1\right){\text{Global}\stackrel{`}{}\text{x}}^6-3\cosh \left(9c_1\right){\text{Global}\stackrel{`}{}\text{x}}^3-3\sinh \left(9c_1\right){\text{Global}\stackrel{`}{}\text{x}}^3+\cosh \left(12c_1\right)+\sinh \left(12c_1\right)}}-\frac{(1+i\sqrt{3})(-9{\text{Global}\stackrel{`}{}\text{x}}^4-72\cosh \left(3c_1\right)\text{Global}\stackrel{`}{}\text{x}-72\sinh \left(3c_1\right)\text{Global}\stackrel{`}{}\text{x})}{72\sqrt[3]{{\text{Global}\stackrel{`}{}\text{x}}^6-20\cosh \left(3c_1\right){\text{Global}\stackrel{`}{}\text{x}}^3-20\sinh \left(3c_1\right){\text{Global}\stackrel{`}{}\text{x}}^3-8\cosh \left(6c_1\right)-8\sinh \left(6c_1\right)+8\sqrt{-\cosh \left(3c_1\right){\text{Global}\stackrel{`}{}\text{x}}^9-\sinh \left(3c_1\right){\text{Global}\stackrel{`}{}\text{x}}^9+3\cosh \left(6c_1\right){\text{Global}\stackrel{`}{}\text{x}}^6+3\sinh \left(6c_1\right){\text{Global}\stackrel{`}{}\text{x}}^6-3\cosh \left(9c_1\right){\text{Global}\stackrel{`}{}\text{x}}^3-3\sinh \left(9c_1\right){\text{Global}\stackrel{`}{}\text{x}}^3+\cosh \left(12c_1\right)+\sinh \left(12c_1\right)}}}\},\{\text{Global}\stackrel{`}{}\text{y}(\text{Global}\stackrel{`}{}\text{x})\to -\frac{{\text{Global}\stackrel{`}{}\text{x}}^2}{4}+\frac{1}{8}(1+i\sqrt{3})\sqrt[3]{{\text{Global}\stackrel{`}{}\text{x}}^6-20\cosh \left(3c_1\right){\text{Global}\stackrel{`}{}\text{x}}^3-20\sinh \left(3c_1\right){\text{Global}\stackrel{`}{}\text{x}}^3-8\cosh \left(6c_1\right)-8\sinh \left(6c_1\right)+8\sqrt{-\cosh \left(3c_1\right){\text{Global}\stackrel{`}{}\text{x}}^9-\sinh \left(3c_1\right){\text{Global}\stackrel{`}{}\text{x}}^9+3\cosh \left(6c_1\right){\text{Global}\stackrel{`}{}\text{x}}^6+3\sinh \left(6c_1\right){\text{Global}\stackrel{`}{}\text{x}}^6-3\cosh \left(9c_1\right){\text{Global}\stackrel{`}{}\text{x}}^3-3\sinh \left(9c_1\right){\text{Global}\stackrel{`}{}\text{x}}^3+\cosh \left(12c_1\right)+\sinh \left(12c_1\right)}}-\frac{(1-i\sqrt{3})(-9{\text{Global}\stackrel{`}{}\text{x}}^4-72\cosh \left(3c_1\right)\text{Global}\stackrel{`}{}\text{x}-72\sinh \left(3c_1\right)\text{Global}\stackrel{`}{}\text{x})}{72\sqrt[3]{{\text{Global}\stackrel{`}{}\text{x}}^6-20\cosh \left(3c_1\right){\text{Global}\stackrel{`}{}\text{x}}^3-20\sinh \left(3c_1\right){\text{Global}\stackrel{`}{}\text{x}}^3-8\cosh \left(6c_1\right)-8\sinh \left(6c_1\right)+8\sqrt{-\cosh \left(3c_1\right){\text{Global}\stackrel{`}{}\text{x}}^9-\sinh \left(3c_1\right){\text{Global}\stackrel{`}{}\text{x}}^9+3\cosh \left(6c_1\right){\text{Global}\stackrel{`}{}\text{x}}^6+3\sinh \left(6c_1\right){\text{Global}\stackrel{`}{}\text{x}}^6-3\cosh \left(9c_1\right){\text{Global}\stackrel{`}{}\text{x}}^3-3\sinh \left(9c_1\right){\text{Global}\stackrel{`}{}\text{x}}^3+\cosh \left(12c_1\right)+\sinh \left(12c_1\right)}}}\},\{\text{Global}\stackrel{`}{}\text{y}(\text{Global}\stackrel{`}{}\text{x})\to -\frac{{\text{Global}\stackrel{`}{}\text{x}}^2}{4}-\frac{1}{4}\sqrt[3]{{\text{Global}\stackrel{`}{}\text{x}}^6+20\cosh \left(3c_1\right){\text{Global}\stackrel{`}{}\text{x}}^3+20\sinh \left(3c_1\right){\text{Global}\stackrel{`}{}\text{x}}^3-8\cosh \left(6c_1\right)-8\sinh \left(6c_1\right)+8\sqrt{\cosh \left(3c_1\right){\text{Global}\stackrel{`}{}\text{x}}^9+\sinh \left(3c_1\right){\text{Global}\stackrel{`}{}\text{x}}^9+3\cosh \left(6c_1\right){\text{Global}\stackrel{`}{}\text{x}}^6+3\sinh \left(6c_1\right){\text{Global}\stackrel{`}{}\text{x}}^6+3\cosh \left(9c_1\right){\text{Global}\stackrel{`}{}\text{x}}^3+3\sinh \left(9c_1\right){\text{Global}\stackrel{`}{}\text{x}}^3+\cosh \left(12c_1\right)+\sinh \left(12c_1\right)}}+\frac{-9{\text{Global}\stackrel{`}{}\text{x}}^4+72\cosh \left(3c_1\right)\text{Global}\stackrel{`}{}\text{x}+72\sinh \left(3c_1\right)\text{Global}\stackrel{`}{}\text{x}}{36\sqrt[3]{{\text{Global}\stackrel{`}{}\text{x}}^6+20\cosh \left(3c_1\right){\text{Global}\stackrel{`}{}\text{x}}^3+20\sinh \left(3c_1\right){\text{Global}\stackrel{`}{}\text{x}}^3-8\cosh \left(6c_1\right)-8\sinh \left(6c_1\right)+8\sqrt{\cosh \left(3c_1\right){\text{Global}\stackrel{`}{}\text{x}}^9+\sinh \left(3c_1\right){\text{Global}\stackrel{`}{}\text{x}}^9+3\cosh \left(6c_1\right){\text{Global}\stackrel{`}{}\text{x}}^6+3\sinh \left(6c_1\right){\text{Global}\stackrel{`}{}\text{x}}^6+3\cosh \left(9c_1\right){\text{Global}\stackrel{`}{}\text{x}}^3+3\sinh \left(9c_1\right){\text{Global}\stackrel{`}{}\text{x}}^3+\cosh \left(12c_1\right)+\sinh \left(12c_1\right)}}}\},\{\text{Global}\stackrel{`}{}\text{y}(\text{Global}\stackrel{`}{}\text{x})\to -\frac{{\text{Global}\stackrel{`}{}\text{x}}^2}{4}+\frac{1}{8}(1-i\sqrt{3})\sqrt[3]{{\text{Global}\stackrel{`}{}\text{x}}^6+20\cosh \left(3c_1\right){\text{Global}\stackrel{`}{}\text{x}}^3+20\sinh \left(3c_1\right){\text{Global}\stackrel{`}{}\text{x}}^3-8\cosh \left(6c_1\right)-8\sinh \left(6c_1\right)+8\sqrt{\cosh \left(3c_1\right){\text{Global}\stackrel{`}{}\text{x}}^9+\sinh \left(3c_1\right){\text{Global}\stackrel{`}{}\text{x}}^9+3\cosh \left(6c_1\right){\text{Global}\stackrel{`}{}\text{x}}^6+3\sinh \left(6c_1\right){\text{Global}\stackrel{`}{}\text{x}}^6+3\cosh \left(9c_1\right){\text{Global}\stackrel{`}{}\text{x}}^3+3\sinh \left(9c_1\right){\text{Global}\stackrel{`}{}\text{x}}^3+\cosh \left(12c_1\right)+\sinh \left(12c_1\right)}}-\frac{(1+i\sqrt{3})(-9{\text{Global}\stackrel{`}{}\text{x}}^4+72\cosh \left(3c_1\right)\text{Global}\stackrel{`}{}\text{x}+72\sinh \left(3c_1\right)\text{Global}\stackrel{`}{}\text{x})}{72\sqrt[3]{{\text{Global}\stackrel{`}{}\text{x}}^6+20\cosh \left(3c_1\right){\text{Global}\stackrel{`}{}\text{x}}^3+20\sinh \left(3c_1\right){\text{Global}\stackrel{`}{}\text{x}}^3-8\cosh \left(6c_1\right)-8\sinh \left(6c_1\right)+8\sqrt{\cosh \left(3c_1\right){\text{Global}\stackrel{`}{}\text{x}}^9+\sinh \left(3c_1\right){\text{Global}\stackrel{`}{}\text{x}}^9+3\cosh \left(6c_1\right){\text{Global}\stackrel{`}{}\text{x}}^6+3\sinh \left(6c_1\right){\text{Global}\stackrel{`}{}\text{x}}^6+3\cosh \left(9c_1\right){\text{Global}\stackrel{`}{}\text{x}}^3+3\sinh \left(9c_1\right){\text{Global}\stackrel{`}{}\text{x}}^3+\cosh \left(12c_1\right)+\sinh \left(12c_1\right)}}}\},\{\text{Global}\stackrel{`}{}\text{y}(\text{Global}\stackrel{`}{}\text{x})\to -\frac{{\text{Global}\stackrel{`}{}\text{x}}^2}{4}+\frac{1}{8}(1+i\sqrt{3})\sqrt[3]{{\text{Global}\stackrel{`}{}\text{x}}^6+20\cosh \left(3c_1\right){\text{Global}\stackrel{`}{}\text{x}}^3+20\sinh \left(3c_1\right){\text{Global}\stackrel{`}{}\text{x}}^3-8\cosh \left(6c_1\right)-8\sinh \left(6c_1\right)+8\sqrt{\cosh \left(3c_1\right){\text{Global}\stackrel{`}{}\text{x}}^9+\sinh \left(3c_1\right){\text{Global}\stackrel{`}{}\text{x}}^9+3\cosh \left(6c_1\right){\text{Global}\stackrel{`}{}\text{x}}^6+3\sinh \left(6c_1\right){\text{Global}\stackrel{`}{}\text{x}}^6+3\cosh \left(9c_1\right){\text{Global}\stackrel{`}{}\text{x}}^3+3\sinh \left(9c_1\right){\text{Global}\stackrel{`}{}\text{x}}^3+\cosh \left(12c_1\right)+\sinh \left(12c_1\right)}}-\frac{(1-i\sqrt{3})(-9{\text{Global}\stackrel{`}{}\text{x}}^4+72\cosh \left(3c_1\right)\text{Global}\stackrel{`}{}\text{x}+72\sinh \left(3c_1\right)\text{Global}\stackrel{`}{}\text{x})}{72\sqrt[3]{{\text{Global}\stackrel{`}{}\text{x}}^6+20\cosh \left(3c_1\right){\text{Global}\stackrel{`}{}\text{x}}^3+20\sinh \left(3c_1\right){\text{Global}\stackrel{`}{}\text{x}}^3-8\cosh \left(6c_1\right)-8\sinh \left(6c_1\right)+8\sqrt{\cosh \left(3c_1\right){\text{Global}\stackrel{`}{}\text{x}}^9+\sinh \left(3c_1\right){\text{Global}\stackrel{`}{}\text{x}}^9+3\cosh \left(6c_1\right){\text{Global}\stackrel{`}{}\text{x}}^6+3\sinh \left(6c_1\right){\text{Global}\stackrel{`}{}\text{x}}^6+3\cosh \left(9c_1\right){\text{Global}\stackrel{`}{}\text{x}}^3+3\sinh \left(9c_1\right){\text{Global}\stackrel{`}{}\text{x}}^3+\cosh \left(12c_1\right)+\sinh \left(12c_1\right)}}}\}\}$$

✓ Maple : cpu = 0.653 (sec), leaf count = 690

$$\{y\left(x\right)={(\frac{1}{2}\sqrt[3]{6\mathit{\_}\mathit{C}\mathit{1}-x^3+2\sqrt{-3x^3\mathit{\_}\mathit{C}\mathit{1}+9{\mathit{\_}\mathit{C}\mathit{1}}^2}}+\frac{x^2}{2}\frac{1}{\sqrt[3]{6\mathit{\_}\mathit{C}\mathit{1}-x^3+2\sqrt{-3x^3\mathit{\_}\mathit{C}\mathit{1}+9{\mathit{\_}\mathit{C}\mathit{1}}^2}}}-\frac{x}{2})}^2+2x(1/2\sqrt[3]{6\mathit{\_}\mathit{C}\mathit{1}-x^3+2\sqrt{-3x^3\mathit{\_}\mathit{C}\mathit{1}+9{\mathit{\_}\mathit{C}\mathit{1}}^2}}+1/2\frac{x^2}{\sqrt[3]{6\mathit{\_}\mathit{C}\mathit{1}-x^3+2\sqrt{-3x^3\mathit{\_}\mathit{C}\mathit{1}+9{\mathit{\_}\mathit{C}\mathit{1}}^2}}}-x/2),y\left(x\right)={(-\frac{1}{4}\sqrt[3]{6\mathit{\_}\mathit{C}\mathit{1}-x^3+2\sqrt{-3x^3\mathit{\_}\mathit{C}\mathit{1}+9{\mathit{\_}\mathit{C}\mathit{1}}^2}}-\frac{x^2}{4}\frac{1}{\sqrt[3]{6\mathit{\_}\mathit{C}\mathit{1}-x^3+2\sqrt{-3x^3\mathit{\_}\mathit{C}\mathit{1}+9{\mathit{\_}\mathit{C}\mathit{1}}^2}}}-\frac{x}{2}-\frac{i}{2}\sqrt{3}(\frac{1}{2}\sqrt[3]{6\mathit{\_}\mathit{C}\mathit{1}-x^3+2\sqrt{-3x^3\mathit{\_}\mathit{C}\mathit{1}+9{\mathit{\_}\mathit{C}\mathit{1}}^2}}-\frac{x^2}{2}\frac{1}{\sqrt[3]{6\mathit{\_}\mathit{C}\mathit{1}-x^3+2\sqrt{-3x^3\mathit{\_}\mathit{C}\mathit{1}+9{\mathit{\_}\mathit{C}\mathit{1}}^2}}}))}^2+2x(-1/4\sqrt[3]{6\mathit{\_}\mathit{C}\mathit{1}-x^3+2\sqrt{-3x^3\mathit{\_}\mathit{C}\mathit{1}+9{\mathit{\_}\mathit{C}\mathit{1}}^2}}-1/4\frac{x^2}{\sqrt[3]{6\mathit{\_}\mathit{C}\mathit{1}-x^3+2\sqrt{-3x^3\mathit{\_}\mathit{C}\mathit{1}+9{\mathit{\_}\mathit{C}\mathit{1}}^2}}}-x/2-i/2\sqrt{3}(1/2\sqrt[3]{6\mathit{\_}\mathit{C}\mathit{1}-x^3+2\sqrt{-3x^3\mathit{\_}\mathit{C}\mathit{1}+9{\mathit{\_}\mathit{C}\mathit{1}}^2}}-1/2\frac{x^2}{\sqrt[3]{6\mathit{\_}\mathit{C}\mathit{1}-x^3+2\sqrt{-3x^3\mathit{\_}\mathit{C}\mathit{1}+9{\mathit{\_}\mathit{C}\mathit{1}}^2}}})),y\left(x\right)={(-\frac{1}{4}\sqrt[3]{6\mathit{\_}\mathit{C}\mathit{1}-x^3+2\sqrt{-3x^3\mathit{\_}\mathit{C}\mathit{1}+9{\mathit{\_}\mathit{C}\mathit{1}}^2}}-\frac{x^2}{4}\frac{1}{\sqrt[3]{6\mathit{\_}\mathit{C}\mathit{1}-x^3+2\sqrt{-3x^3\mathit{\_}\mathit{C}\mathit{1}+9{\mathit{\_}\mathit{C}\mathit{1}}^2}}}-\frac{x}{2}+\frac{i}{2}\sqrt{3}(\frac{1}{2}\sqrt[3]{6\mathit{\_}\mathit{C}\mathit{1}-x^3+2\sqrt{-3x^3\mathit{\_}\mathit{C}\mathit{1}+9{\mathit{\_}\mathit{C}\mathit{1}}^2}}-\frac{x^2}{2}\frac{1}{\sqrt[3]{6\mathit{\_}\mathit{C}\mathit{1}-x^3+2\sqrt{-3x^3\mathit{\_}\mathit{C}\mathit{1}+9{\mathit{\_}\mathit{C}\mathit{1}}^2}}}))}^2+2x(-1/4\sqrt[3]{6\mathit{\_}\mathit{C}\mathit{1}-x^3+2\sqrt{-3x^3\mathit{\_}\mathit{C}\mathit{1}+9{\mathit{\_}\mathit{C}\mathit{1}}^2}}-1/4\frac{x^2}{\sqrt[3]{6\mathit{\_}\mathit{C}\mathit{1}-x^3+2\sqrt{-3x^3\mathit{\_}\mathit{C}\mathit{1}+9{\mathit{\_}\mathit{C}\mathit{1}}^2}}}-x/2+i/2\sqrt{3}(1/2\sqrt[3]{6\mathit{\_}\mathit{C}\mathit{1}-x^3+2\sqrt{-3x^3\mathit{\_}\mathit{C}\mathit{1}+9{\mathit{\_}\mathit{C}\mathit{1}}^2}}-1/2\frac{x^2}{\sqrt[3]{6\mathit{\_}\mathit{C}\mathit{1}-x^3+2\sqrt{-3x^3\mathit{\_}\mathit{C}\mathit{1}+9{\mathit{\_}\mathit{C}\mathit{1}}^2}}}))\}$$