2.675   ODE No. 675

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

$$y^{\prime }(x)=\frac{a{x}^4+a{e}^x{x}^3+a{x}^3-x^{2}y(x{)}^2-e^{x}xy(x{)}^2-xy(x{)}^2+y(x)}{x}$$ ✓ Mathematica : cpu = 0.0498359 (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 = 0.047 (sec), leaf count = 46

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