2.412   ODE No. 412

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

$$\text{Global}\stackrel{`}{}\text{a}+\text{Global}\stackrel{`}{}\text{x}{\text{Global}\stackrel{`}{}\text{y}}^{\prime }(\text{Global}\stackrel{`}{}\text{x}{)}^2+\text{Global}\stackrel{`}{}\text{y}(\text{Global}\stackrel{`}{}\text{x}){\text{Global}\stackrel{`}{}\text{y}}^{\prime }(\text{Global}\stackrel{`}{}\text{x})=0$$ ✓ Mathematica : cpu = 27.0817 (sec), leaf count = 16145

$$\text{too large to display}$$

✓ Maple : cpu = 0.04 (sec), leaf count = 146

$$\{-x^2\mathit{\_}\mathit{C}\mathit{1}{\left(\frac{1}{x}(-y\left(x\right)+\sqrt{{\left(y\left(x\right)\right)}^2-4ax})\right)}^{\frac{3}{2}}{(-y\left(x\right)+\sqrt{{\left(y\left(x\right)\right)}^2-4ax})}^{-2}+x+\frac{4a{x}^2}{3}{(-y\left(x\right)+\sqrt{{\left(y\left(x\right)\right)}^2-4ax})}^{-2}=0,x^2\mathit{\_}\mathit{C}\mathit{1}{\left(\frac{1}{x}(-2y\left(x\right)-2\sqrt{{\left(y\left(x\right)\right)}^2-4ax})\right)}^{\frac{3}{2}}{(y\left(x\right)+\sqrt{{\left(y\left(x\right)\right)}^2-4ax})}^{-2}+x+\frac{4a{x}^2}{3}{(y\left(x\right)+\sqrt{{\left(y\left(x\right)\right)}^2-4ax})}^{-2}=0\}$$