3.457   ODE No. 457

$$\boxed{{\displaystyle x^4{\left(\frac{\mathrm{d}}{\mathrm{d}x}y\left(x\right)\right)}^2-x\frac{\mathrm{d}}{\mathrm{d}x}y\left(x\right)-y\left(x\right)=0}}$$

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

Mathematica: cpu = 0.948120 (sec), leaf count = 410 $$\{\text{Solve}[\frac{x\sqrt{4x^{2}y(x)+1}(\log (x)-\log (\sqrt{4x^{2}y(x)+1}+1))}{\sqrt{4x^{4}y(x)+x^2}}+\frac{x\sqrt{4x^{2}y(x)+1}\log (y(x))-x\sqrt{4x^{2}y(x)+1}\log (4x^{2}y(x)+1)+\sqrt{4x^{4}y(x)+x^2}\log (\frac{1}{4x^{2}y(x)}+1)-\sqrt{4x^{4}y(x)+x^2}\log (4x^{2}y(x)+1)+x\sqrt{4x^{2}y(x)+1}\log (4x^{3}y(x)+x)}{2\sqrt{4x^{4}y(x)+x^2}}=c_1,y(x)],\text{Solve}[-\frac{x\sqrt{4x^{2}y(x)+1}(\log (x)-\log (\sqrt{4x^{2}y(x)+1}+1))}{\sqrt{4x^{4}y(x)+x^2}}-\frac{x\sqrt{4x^{2}y(x)+1}\log (y(x))-x\sqrt{4x^{2}y(x)+1}\log (4x^{2}y(x)+1)-\sqrt{4x^{4}y(x)+x^2}\log (\frac{1}{4x^{2}y(x)}+1)+\sqrt{4x^{4}y(x)+x^2}\log (4x^{2}y(x)+1)+x\sqrt{4x^{2}y(x)+1}\log (4x^{3}y(x)+x)}{2\sqrt{4x^{4}y(x)+x^2}}=c_1,y(x)]\}$$

Maple: cpu = 1.186 (sec), leaf count = 135 $$\{y\left(x\right)=-\frac{1}{4x^2},y\left(x\right)=\frac{-\mathit{\_}\mathit{C}\mathit{1}(-\mathit{\_}\mathit{C}\mathit{1}-2ix)-{\mathit{\_}\mathit{C}\mathit{1}}^2-2x^2}{2{\mathit{\_}\mathit{C}\mathit{1}}^2{x}^2},y\left(x\right)=\frac{-\mathit{\_}\mathit{C}\mathit{1}(-\mathit{\_}\mathit{C}\mathit{1}+2ix)-{\mathit{\_}\mathit{C}\mathit{1}}^2-2x^2}{2{\mathit{\_}\mathit{C}\mathit{1}}^2{x}^2},y\left(x\right)=\frac{\mathit{\_}\mathit{C}\mathit{1}(\mathit{\_}\mathit{C}\mathit{1}-2ix)-2x^2-{\mathit{\_}\mathit{C}\mathit{1}}^2}{2{\mathit{\_}\mathit{C}\mathit{1}}^2{x}^2},y\left(x\right)=\frac{\mathit{\_}\mathit{C}\mathit{1}(\mathit{\_}\mathit{C}\mathit{1}+2ix)-2x^2-{\mathit{\_}\mathit{C}\mathit{1}}^2}{2{\mathit{\_}\mathit{C}\mathit{1}}^2{x}^2}\}$$