3.709   ODE No. 709

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

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

Mathematica: cpu = 5.563707 (sec), leaf count = 217 $$\{\{y(x)\to -\frac{1}{6}\sqrt{144ax-24c_1{x}^3+36c_1{x}^2-72c_{1}x+72c_1\log (x+1)-36c_1^2-4x^6+12x^5-33x^4+36x^3+24x^3\log (x+1)-36x^2-36x^2\log (x+1)-36{\log }^2(x+1)+72x\log (x+1)}\},\{y(x)\to \frac{1}{6}\sqrt{144ax-24c_1{x}^3+36c_1{x}^2-72c_{1}x+72c_1\log (x+1)-36c_1^2-4x^6+12x^5-33x^4+36x^3+24x^3\log (x+1)-36x^2-36x^2\log (x+1)-36{\log }^2(x+1)+72x\log (x+1)}\}\}$$

Maple: cpu = 0.203 (sec), leaf count = 39 $$\{-\sqrt{-{\left(y\left(x\right)\right)}^2+4ax}-\frac{x^3}{3}+\frac{x^2}{2}-x+\ln (1+x)-\mathit{\_}\mathit{C}\mathit{1}=0\}$$