2.457   ODE No. 457

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

$$x^4{y}^{\prime }(x{)}^2-x{y}^{\prime }(x)-y(x)=0$$ ✓ Mathematica : cpu = 0.243138 (sec), leaf count = 118

$$\{\text{Solve}[-\frac{x\sqrt{4x^{2}y(x)+1}{\tanh }^{-1}\left(\sqrt{4x^{2}y(x)+1}\right)}{\sqrt{4x^{4}y(x)+x^2}}-\frac{1}{2}\log (y(x))=c_1,y(x)],\text{Solve}[\frac{x\sqrt{4x^{2}y(x)+1}{\tanh }^{-1}\left(\sqrt{4x^{2}y(x)+1}\right)}{\sqrt{4x^{4}y(x)+x^2}}-\frac{1}{2}\log (y(x))=c_1,y(x)]\}$$ ✓ Maple : cpu = 3.827 (sec), leaf count = 45

$$\{y\left(x\right)=\frac{i\mathit{\_}\mathit{C}\mathit{1}-x}{x{\mathit{\_}\mathit{C}\mathit{1}}^2},y\left(x\right)=\frac{-i\mathit{\_}\mathit{C}\mathit{1}-x}{x{\mathit{\_}\mathit{C}\mathit{1}}^2},y\left(x\right)=-\frac{1}{4x^2}\}$$