2.467   ODE No. 467

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

$$y(x)y^{\prime }(x{)}^2-4x{y}^{\prime }(x)+y(x)=0$$ ✓ Mathematica : cpu = 0.262129 (sec), leaf count = 226

$$\left\{\{y(x)\to \sqrt{x^2+\frac{22^{2/3}{x}^4}{\sqrt[3]{32x^6-40c_1{}^3{x}^3+\sqrt{-48c_1{}^9{x}^3+768c_1{}^6{x}^6-4096c_1{}^3{x}^9+c_1{}^{12}}-c_1{}^6}}+\frac{2^{2/3}{c}_1{}^{3}x}{\sqrt[3]{32x^6-40c_1{}^3{x}^3+\sqrt{-48c_1{}^9{x}^3+768c_1{}^6{x}^6-4096c_1{}^3{x}^9+c_1{}^{12}}-c_1{}^6}}+\frac{\sqrt[3]{32x^6-40c_1{}^3{x}^3+\sqrt{-48c_1{}^9{x}^3+768c_1{}^6{x}^6-4096c_1{}^3{x}^9+c_1{}^{12}}-c_1{}^6}}{22^{2/3}}}\}\right\}$$ ✓ Maple : cpu = 0.135 (sec), leaf count = 148

$$\{-\frac{\mathit{\_}\mathit{C}\mathit{1}x}{y\left(x\right)}\frac{1}{\sqrt[3]{\frac{1}{{\left(y\left(x\right)\right)}^2}(8x^2-4{\left(y\left(x\right)\right)}^2-4x\sqrt{4x^2-{\left(y\left(x\right)\right)}^2})}}\frac{1}{\sqrt[3]{\frac{1}{y\left(x\right)}(2x-\sqrt{4x^2-{\left(y\left(x\right)\right)}^2})}}+x=0,-\frac{\mathit{\_}\mathit{C}\mathit{1}x}{y\left(x\right)}\frac{1}{\sqrt[3]{\frac{1}{{\left(y\left(x\right)\right)}^2}(x\sqrt{4x^2-{\left(y\left(x\right)\right)}^2}+2x^2-{\left(y\left(x\right)\right)}^2)}}\frac{1}{\sqrt[3]{\frac{1}{y\left(x\right)}(2x+\sqrt{4x^2-{\left(y\left(x\right)\right)}^2})}}+x=0\}$$