4.230   ODE No. 1230

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

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

Mathematica: cpu = 0.025503 (sec), leaf count = 82 $$\left\{\{y(x)\to c_1{(x^2+1)}^{\frac{2-a}{4}}{P}_{\frac{a-4}{2}}^{\frac{a-2}{2}}(ix)+c_2{(x^2+1)}^{\frac{2-a}{4}}{Q}_{\frac{a-4}{2}}^{\frac{a-2}{2}}(ix)\}\right\}$$

Maple: cpu = 0.062 (sec), leaf count = 36 $$\{y\left(x\right)=\mathit{\_}\mathit{C}\mathit{1}{(x^2+1)}^{1-\frac{a}{2}}+\mathit{\_}\mathit{C}\mathit{2}{}_2\text{F}{}_1(1,\frac{a}{2}-\frac{1}{2};\frac{3}{2};-x^2)x\}$$