2.1368   ODE No. 1368

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

$$y^{″}(x)=-\frac{ax{y}^{\prime }(x)}{x^2+1}-\frac{by(x)}{{(x^2+1)}^2}$$ ✓ Mathematica : cpu = 0.0278908 (sec), leaf count = 106

$$\left\{\{y(x)\to c_1{(x^2+1)}^{\frac{2-a}{4}}{P}_{\frac{a-2}{2}}^{\frac{1}{2}\sqrt{a^2-4a+4b+4}}(ix)+c_2{(x^2+1)}^{\frac{2-a}{4}}{Q}_{\frac{a-2}{2}}^{\frac{1}{2}\sqrt{a^2-4a+4b+4}}(ix)\}\right\}$$

✓ Maple : cpu = 0.093 (sec), leaf count = 81

$$\{y\left(x\right)=\mathit{\_}\mathit{C}\mathit{1}{(x^2+1)}^{\frac{1}{2}-\frac{a}{4}}\mathit{L}\mathit{e}\mathit{g}\mathit{e}\mathit{n}\mathit{d}\mathit{r}\mathit{e}\mathit{P}(\frac{a}{2}-1,\frac{1}{2}\sqrt{a^2-4a+4b+4},ix)+\mathit{\_}\mathit{C}\mathit{2}{(x^2+1)}^{\frac{1}{2}-\frac{a}{4}}\mathit{L}\mathit{e}\mathit{g}\mathit{e}\mathit{n}\mathit{d}\mathit{r}\mathit{e}\mathit{Q}(\frac{a}{2}-1,\frac{1}{2}\sqrt{a^2-4a+4b+4},ix)\}$$