3.431   ODE No. 431

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

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

Mathematica: cpu = 0.037005 (sec), leaf count = 111 $$\{\{y(x)\to \sqrt{{\tan }^2(c_1-\log (x))+1}(-\cot (c_1-\log (x)))\},\{y(x)\to \sqrt{{\tan }^2(c_1-\log (x))+1}\cot (c_1-\log (x))\},\{y(x)\to \sqrt{{\tan }^2(c_1+\log (x))+1}(-\cot (c_1+\log (x)))\},\{y(x)\to \sqrt{{\tan }^2(c_1+\log (x))+1}\cot (c_1+\log (x))\}\}$$

Maple: cpu = 0.561 (sec), leaf count = 62 $$\{y\left(x\right)=-1,y\left(x\right)=1,y\left(x\right)=\frac{1}{\tan (-\ln \left(x\right)+\mathit{\_}\mathit{C}\mathit{1})}\sqrt{{(\tan (-\ln \left(x\right)+\mathit{\_}\mathit{C}\mathit{1}))}^2+1},y\left(x\right)=-\frac{1}{\tan (-\ln \left(x\right)+\mathit{\_}\mathit{C}\mathit{1})}\sqrt{{(\tan (-\ln \left(x\right)+\mathit{\_}\mathit{C}\mathit{1}))}^2+1}\}$$