3.677   ODE No. 677

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

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

Mathematica: cpu = 0.037505 (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 = 0.047 (sec), leaf count = 64 $$\{y\left(x\right)=\tanh (\frac{\ln (1+x)x^2}{2}\sqrt{a}+\frac{x^3}{3}\sqrt{a}+\frac{x^2}{4}\sqrt{a}-\frac{\ln (1+x)}{2}\sqrt{a}+\mathit{\_}\mathit{C}\mathit{1}\sqrt{a}+\frac{x}{2}\sqrt{a}+\frac{3}{4}\sqrt{a})x\sqrt{a}\}$$