3.712   ODE No. 712

$$\boxed{{\displaystyle \frac{\mathrm{d}}{\mathrm{d}x}y\left(x\right)=1/2\frac{x^2+2x+1+2x^3\sqrt{x^2+2x+1-4y\left(x\right)}}{1+x}=0}}$$

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

Mathematica: cpu = 0.296038 (sec), leaf count = 115 $$\left\{\{y(x)\to \frac{1}{36}(24c_1{x}^3-36c_1{x}^2+72c_{1}x-72c_1\log (x+1)-36c_1^2+132c_1-4x^6+12x^5-33x^4-8x^3+24x^3\log (x+1)+39x^2-36x^2\log (x+1)-114x-36{\log }^2(x+1)+72x\log (x+1)+132\log (x+1)-112)\}\right\}$$

Maple: cpu = 0.265 (sec), leaf count = 38 $$\{\mathit{\_}\mathit{C}\mathit{1}-\frac{2x^3}{3}+x^2-2x+2\ln (1+x)-\sqrt{x^2+2x+1-4y\left(x\right)}=0\}$$