2.296   ODE No. 296

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

$$x^4+x(x^{2}y(x)+x^2+y(x{)}^2)y^{\prime }(x)-2x^{2}y(x{)}^2-2y(x{)}^3=0$$ ✓ Mathematica : cpu = 0.620665 (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 = 0.73 (sec), leaf count = 165

$$\{y\left(x\right)=-x^3(x-2)(\frac{1}{x^2(x-2)}(\mathit{\_}\mathit{C}\mathit{1}x-x^2-\sqrt{-\mathit{\_}\mathit{C}\mathit{1}{x}^4+{\mathit{\_}\mathit{C}\mathit{1}}^2{x}^2+x^4})-1){(\mathit{\_}\mathit{C}\mathit{1}x-x^2-\sqrt{-\mathit{\_}\mathit{C}\mathit{1}{x}^4+{\mathit{\_}\mathit{C}\mathit{1}}^2{x}^2+x^4})}^{-1},y\left(x\right)=-x^3(x-2)(\frac{1}{x^2(x-2)}(\mathit{\_}\mathit{C}\mathit{1}x-x^2+\sqrt{-\mathit{\_}\mathit{C}\mathit{1}{x}^4+{\mathit{\_}\mathit{C}\mathit{1}}^2{x}^2+x^4})-1){(\mathit{\_}\mathit{C}\mathit{1}x-x^2+\sqrt{-\mathit{\_}\mathit{C}\mathit{1}{x}^4+{\mathit{\_}\mathit{C}\mathit{1}}^2{x}^2+x^4})}^{-1}\}$$