4.127   ODE No. 1127

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

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

Mathematica: cpu = 0.038505 (sec), leaf count = 36 $$\left\{\{y(x)\to c_1{e}^{ax}{x}^{-ax}+c_2{e}^{ax}{x}^{-ax}\log (x)\}\right\}$$

Maple: cpu = 0.016 (sec), leaf count = 31 $$\{y\left(x\right)=\mathit{\_}\mathit{C}\mathit{1}{x}^{-ax}{\mathrm{e}}^{ax}+\mathit{\_}\mathit{C}\mathit{2}{x}^{-ax}{\mathrm{e}}^{ax}\ln \left(x\right)\}$$