3.302   ODE No. 302

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

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

Mathematica: cpu = 0.016002 (sec), leaf count = 70 $$\{\{y(x)\to \frac{c_{1}x-\sqrt{x}\sqrt{c_1^{2}x+4}}{2x}\},\{y(x)\to \frac{c_{1}x+\sqrt{x}\sqrt{c_1^{2}x+4}}{2x}\}\}$$

Maple: cpu = 0.109 (sec), leaf count = 137 $$\{y\left(x\right)=-\frac{1}{2\mathit{\_}\mathit{C}\mathit{1}x}\sqrt{-2x\mathit{\_}\mathit{C}\mathit{1}(-2\mathit{\_}\mathit{C}\mathit{1}-x+\sqrt{4\mathit{\_}\mathit{C}\mathit{1}x+x^2})},y\left(x\right)=\frac{1}{2\mathit{\_}\mathit{C}\mathit{1}x}\sqrt{-2x\mathit{\_}\mathit{C}\mathit{1}(-2\mathit{\_}\mathit{C}\mathit{1}-x+\sqrt{4\mathit{\_}\mathit{C}\mathit{1}x+x^2})},y\left(x\right)=-\frac{\sqrt{2}}{2\mathit{\_}\mathit{C}\mathit{1}x}\sqrt{x\mathit{\_}\mathit{C}\mathit{1}(2\mathit{\_}\mathit{C}\mathit{1}+x+\sqrt{4\mathit{\_}\mathit{C}\mathit{1}x+x^2})},y\left(x\right)=\frac{\sqrt{2}}{2\mathit{\_}\mathit{C}\mathit{1}x}\sqrt{x\mathit{\_}\mathit{C}\mathit{1}(2\mathit{\_}\mathit{C}\mathit{1}+x+\sqrt{4\mathit{\_}\mathit{C}\mathit{1}x+x^2})}\}$$