2.677   ODE No. 677

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

$$y^{\prime }(x)=\frac{a{x}^4+a{x}^3+a{x}^3\log (x+1)-x^{2}y(x{)}^2-xy(x{)}^2+y(x)-xy(x{)}^2\log (x+1)}{x}$$ ✓ Mathematica : cpu = 0.0318496 (sec), leaf count = 80

$$\left\{\{y(x)\to \sqrt{a}x\tanh \left(\frac{1}{12}(12\sqrt{a}{c}_1+4\sqrt{a}{x}^3+3\sqrt{a}{x}^2+6\sqrt{a}{x}^2\log (x+1)+6\sqrt{a}x-6\sqrt{a}\log (x+1))\right)\}\right\}$$

✓ Maple : cpu = 0.041 (sec), leaf count = 64

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