2.468   ODE No. 468

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

$$-4a^{2}x{y}^{\prime }(x)+a^{2}y(x)+y(x)y^{\prime }(x{)}^2=0$$ ✓ Mathematica : cpu = 3.46331 (sec), leaf count = 609

$$\{\text{Solve}[\frac{-4(\frac{y(x{)}^2}{x^2}-4a^2){\tanh }^{-1}\left(\frac{\sqrt{4a^2-\frac{y(x{)}^2}{x^2}}}{2a}\right)+2(\frac{y(x{)}^2}{x^2}-4a^2){\tanh }^{-1}\left(\frac{\sqrt{4a^2-\frac{y(x{)}^2}{x^2}}}{a}\right)+\sqrt{2a-\frac{y(x)}{x}}\sqrt{4a^2-\frac{y(x{)}^2}{x^2}}(\sqrt{2a+\frac{y(x)}{x}}(\log (3a^2-\frac{y(x{)}^2}{x^2})+8{\tan }^{-1}\left(\frac{\sqrt{2a-\frac{y(x)}{x}}}{\sqrt{2a+\frac{y(x)}{x}}}\right)+4\log \left(\frac{y(x)}{x}\right))-8\sqrt{a}\sqrt{\frac{y(x)}{ax}+2}{\sin }^{-1}\left(\frac{\sqrt{2a-\frac{y(x)}{x}}}{2\sqrt{a}}\right))}{6\sqrt{2a-\frac{y(x)}{x}}\sqrt{2a+\frac{y(x)}{x}}\sqrt{4a^2-\frac{y(x{)}^2}{x^2}}}=-\log (x)+c_1,y(x)],\text{Solve}[\frac{4(\frac{y(x{)}^2}{x^2}-4a^2){\tanh }^{-1}\left(\frac{\sqrt{4a^2-\frac{y(x{)}^2}{x^2}}}{2a}\right)-2(\frac{y(x{)}^2}{x^2}-4a^2){\tanh }^{-1}\left(\frac{\sqrt{4a^2-\frac{y(x{)}^2}{x^2}}}{a}\right)+\sqrt{2a-\frac{y(x)}{x}}\sqrt{4a^2-\frac{y(x{)}^2}{x^2}}(\sqrt{2a+\frac{y(x)}{x}}(\log (3a^2-\frac{y(x{)}^2}{x^2})-8{\tan }^{-1}\left(\frac{\sqrt{2a-\frac{y(x)}{x}}}{\sqrt{2a+\frac{y(x)}{x}}}\right)+4\log \left(\frac{y(x)}{x}\right))+8\sqrt{a}\sqrt{\frac{y(x)}{ax}+2}{\sin }^{-1}\left(\frac{\sqrt{2a-\frac{y(x)}{x}}}{2\sqrt{a}}\right))}{6\sqrt{2a-\frac{y(x)}{x}}\sqrt{2a+\frac{y(x)}{x}}\sqrt{4a^2-\frac{y(x{)}^2}{x^2}}}=-\log (x)+c_1,y(x)]\}$$ ✓ Maple : cpu = 0.167 (sec), leaf count = 181

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