2.648   ODE No. 648

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

$$y^{\prime }(x)=-\frac{\sqrt{a}{x}^3(-2\sqrt{a{x}^4+8y(x)}+\sqrt{a}x+\sqrt{a})}{2(x+1)}$$ ✓ Mathematica : cpu = 0.502292 (sec), leaf count = 128

$$\left\{\{y(x)\to \frac{1}{72}(16a{x}^6-48a{x}^5+123a{x}^4-72a{x}^2-96a{x}^3\log (x+1)+144a{x}^2\log (x+1)-96a{c}_1{x}^3+144a{c}_1{x}^2+432ax+144a{\log }^2(x+1)-288ax\log (x+1)-432a\log (x+1)-288a{c}_{1}x+288a{c}_1\log (x+1)+324a+144a{c}_1{}^2-432a{c}_1)\}\right\}$$ ✓ Maple : cpu = 1.187 (sec), leaf count = 41

$$\{\frac{1}{4}\sqrt{a{x}^4+8y\left(x\right)}\frac{1}{\sqrt{a}}-\frac{x^3}{3}+\frac{x^2}{2}-x+\ln (1+x)-\mathit{\_}\mathit{C}\mathit{1}=0\}$$