4.72   ODE No. 1072

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

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

Mathematica: cpu = 0.281536 (sec), leaf count = 38 $$\text{DSolve}[y(x)(-4anp(x{)}^2+a+bp(x))+a{p}^{″}(x)y^{\prime }(x)+y^{″}(x)=0,y(x),x]$$

Maple: cpu = 0.250 (sec), leaf count = 45 $$\{y\left(x\right)=\mathit{D}\mathit{E}\mathit{S}\mathit{o}\mathit{l}(\{\frac{{\mathrm{d}}^2}{\mathrm{d}{x}^2}\mathit{\_}\mathit{Y}\left(x\right)+a\left(\frac{{\mathrm{d}}^2}{\mathrm{d}{x}^2}p\left(x\right)\right)\frac{\mathrm{d}}{\mathrm{d}x}\mathit{\_}\mathit{Y}\left(x\right)+(a+bp\left(x\right)-4na{\left(p\left(x\right)\right)}^2)\mathit{\_}\mathit{Y}\left(x\right)\},\left\{\mathit{\_}\mathit{Y}\left(x\right)\right\})\}$$