4.205   ODE No. 1205

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

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

Mathematica: cpu = 0.212527 (sec), leaf count = 29 $$\text{DSolve}[a{x}^2{y}^{\prime }(x)+f(x)y(x)+x^2{y}^{″}(x)=0,y(x),x]$$

Maple: cpu = 0.0 (sec), leaf count = 30 $$\{y\left(x\right)=\mathit{D}\mathit{E}\mathit{S}\mathit{o}\mathit{l}(\{\frac{f\left(x\right)\mathit{\_}\mathit{Y}\left(x\right)}{x^2}+a\frac{\mathrm{d}}{\mathrm{d}x}\mathit{\_}\mathit{Y}\left(x\right)+\frac{{\mathrm{d}}^2}{\mathrm{d}{x}^2}\mathit{\_}\mathit{Y}\left(x\right)\},\left\{\mathit{\_}\mathit{Y}\left(x\right)\right\})\}$$