4.357   ODE No. 1357

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

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

Mathematica: cpu = 0.665585 (sec), leaf count = 288 $$\left\{\{y(x)\to c_1{x}^{\frac{1}{2}(-\sqrt{a^2-4a-4c+4}-a+2)}{}_2{F}_1(-\frac{1}{4}\sqrt{a^2-2a-4b+1}-\frac{1}{4}\sqrt{a^2-4a-4c+4}+\frac{1}{4},\frac{1}{4}\sqrt{a^2-2a-4b+1}-\frac{1}{4}\sqrt{a^2-4a-4c+4}+\frac{1}{4};1-\frac{1}{2}\sqrt{a^2-4a-4c+4};-x^2)+c_2{x}^{\frac{1}{2}(\sqrt{a^2-4a-4c+4}-a+2)}{}_2{F}_1(-\frac{1}{4}\sqrt{a^2-2a-4b+1}+\frac{1}{4}\sqrt{a^2-4a-4c+4}+\frac{1}{4},\frac{1}{4}\sqrt{a^2-2a-4b+1}+\frac{1}{4}\sqrt{a^2-4a-4c+4}+\frac{1}{4};\frac{1}{2}\sqrt{a^2-4a-4c+4}+1;-x^2)\}\right\}$$

Maple: cpu = 0.094 (sec), leaf count = 103 $$\{y\left(x\right)=\mathit{\_}\mathit{C}\mathit{1}{x}^{1-\frac{a}{2}}\mathit{L}\mathit{e}\mathit{g}\mathit{e}\mathit{n}\mathit{d}\mathit{r}\mathit{e}\mathit{P}(-\frac{1}{2}+\frac{1}{2}\sqrt{a^2-2a-4b+1},\frac{1}{2}\sqrt{a^2-4a-4c+4},\sqrt{x^2+1})+\mathit{\_}\mathit{C}\mathit{2}{x}^{1-\frac{a}{2}}\mathit{L}\mathit{e}\mathit{g}\mathit{e}\mathit{n}\mathit{d}\mathit{r}\mathit{e}\mathit{Q}(-\frac{1}{2}+\frac{1}{2}\sqrt{a^2-2a-4b+1},\frac{1}{2}\sqrt{a^2-4a-4c+4},\sqrt{x^2+1})\}$$