3.279   ODE No. 279

$$\boxed{{\displaystyle ({\left(y\left(x\right)\right)}^2+2y\left(x\right)+x)\frac{\mathrm{d}}{\mathrm{d}x}y\left(x\right)+{(y\left(x\right)+x)}^2{\left(y\left(x\right)\right)}^2+y\left(x\right)(1+y\left(x\right))=0}}$$

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

Mathematica: cpu = 0.624079 (sec), leaf count = 107 $$\{\{y(x)\to \frac{-\sqrt{(-c_{1}x+x^2-1){}^2+4(x-c_1)}+c_{1}x-x^2+1}{2(x-c_1)}\},\{y(x)\to \frac{\sqrt{(-c_{1}x+x^2-1){}^2+4(x-c_1)}+c_{1}x-x^2+1}{2(x-c_1)}\}\}$$

Maple: cpu = 0.140 (sec), leaf count = 120 $$\{y\left(x\right)=\frac{1}{2\mathit{\_}\mathit{C}\mathit{1}-4x}(-\mathit{\_}\mathit{C}\mathit{1}x+2x^2-2+\sqrt{{\mathit{\_}\mathit{C}\mathit{1}}^2{x}^2-4x^3\mathit{\_}\mathit{C}\mathit{1}+4x^4+4\mathit{\_}\mathit{C}\mathit{1}x-8x^2-8\mathit{\_}\mathit{C}\mathit{1}+16x+4}),y\left(x\right)=-\frac{1}{2\mathit{\_}\mathit{C}\mathit{1}-4x}(\mathit{\_}\mathit{C}\mathit{1}x-2x^2+\sqrt{{\mathit{\_}\mathit{C}\mathit{1}}^2{x}^2-4x^3\mathit{\_}\mathit{C}\mathit{1}+4x^4+4\mathit{\_}\mathit{C}\mathit{1}x-8x^2-8\mathit{\_}\mathit{C}\mathit{1}+16x+4}+2)\}$$