4.346   ODE No. 1346

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

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

Mathematica: cpu = 0.326541 (sec), leaf count = 87 $$\left\{\{y(x)\to c_{1}x{e}^{-\frac{-\sqrt{(a-b{)}^2}+a+b}{2x}}+\frac{c_{2}x{e}^{-\frac{\sqrt{(a-b{)}^2}}{2x}-\frac{a}{2x}-\frac{b}{2x}}}{\sqrt{(a-b{)}^2}}\}\right\}$$

Maple: cpu = 0.047 (sec), leaf count = 25 $$\{y\left(x\right)=\mathit{\_}\mathit{C}\mathit{1}x{\mathrm{e}}^{-\frac{a}{x}}+\mathit{\_}\mathit{C}\mathit{2}x{\mathrm{e}}^{-\frac{b}{x}}\}$$