3.675   ODE No. 675

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

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

Mathematica: cpu = 0.057007 (sec), leaf count = 48 $$\left\{\{y(x)\to \sqrt{a}x\tanh \left(\frac{1}{6}\sqrt{a}(6c_1+2x^3+3x^2+6e^{x}x-6e^x)\right)\}\right\}$$

Maple: cpu = 0.031 (sec), leaf count = 46 $$\{y\left(x\right)=\tanh (\frac{x^3}{3}\sqrt{a}+x{\mathrm{e}}^x\sqrt{a}+\frac{x^2}{2}\sqrt{a}-{\mathrm{e}}^x\sqrt{a}+\mathit{\_}\mathit{C}\mathit{1}\sqrt{a})x\sqrt{a}\}$$