4.391   ODE No. 1391

$$\boxed{{\displaystyle \frac{{\mathrm{d}}^2}{\mathrm{d}{x}^2}y\left(x\right)=\frac{(7a{x}^2+5)\frac{\mathrm{d}}{\mathrm{d}x}y\left(x\right)}{x(a{x}^2+1)}-\frac{(15a{x}^2+5)y\left(x\right)}{x^2(a{x}^2+1)}=0}}$$

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

Mathematica: cpu = 0.057507 (sec), leaf count = 27 $$\left\{\{y(x)\to c_1{x}^5-\frac{1}{4}{c}_{2}x(2a{x}^2+1)\}\right\}$$

Maple: cpu = 0.032 (sec), leaf count = 20 $$\{y\left(x\right)=\mathit{\_}\mathit{C}\mathit{1}{x}^5+\mathit{\_}\mathit{C}\mathit{2}(2a{x}^3+x)\}$$