3.296   ODE No. 296

$$\boxed{{\displaystyle x({\left(y\left(x\right)\right)}^2+x^{2}y\left(x\right)+x^2)\frac{\mathrm{d}}{\mathrm{d}x}y\left(x\right)-2{\left(y\left(x\right)\right)}^3-2x^2{\left(y\left(x\right)\right)}^2+x^4=0}}$$

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

Mathematica: cpu = 0.571072 (sec), leaf count = 102 $$\{\{y(x)\to -e^{-c_1}{x}^2-e^{-c_1}\sqrt{-e^{c_1}{x}^4+e^{2c_1}{x}^2+x^4}\},\{y(x)\to e^{-c_1}\sqrt{-e^{c_1}{x}^4+e^{2c_1}{x}^2+x^4}-e^{-c_1}{x}^2\}\}$$

Maple: cpu = 0.562 (sec), leaf count = 165 $$\{y\left(x\right)=-x^3(x-2)(\frac{1}{(x-2)x^2}(\mathit{\_}\mathit{C}\mathit{1}x-x^2-\sqrt{-\mathit{\_}\mathit{C}\mathit{1}{x}^4+{\mathit{\_}\mathit{C}\mathit{1}}^2{x}^2+x^4})-1){(\mathit{\_}\mathit{C}\mathit{1}x-x^2-\sqrt{-\mathit{\_}\mathit{C}\mathit{1}{x}^4+{\mathit{\_}\mathit{C}\mathit{1}}^2{x}^2+x^4})}^{-1},y\left(x\right)=-x^3(x-2)(\frac{1}{(x-2)x^2}(\mathit{\_}\mathit{C}\mathit{1}x-x^2+\sqrt{-\mathit{\_}\mathit{C}\mathit{1}{x}^4+{\mathit{\_}\mathit{C}\mathit{1}}^2{x}^2+x^4})-1){(\mathit{\_}\mathit{C}\mathit{1}x-x^2+\sqrt{-\mathit{\_}\mathit{C}\mathit{1}{x}^4+{\mathit{\_}\mathit{C}\mathit{1}}^2{x}^2+x^4})}^{-1}\}$$