4.318   ODE No. 1318

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

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

Mathematica: cpu = 0.293537 (sec), leaf count = 172 $$\left\{\{y(x)\to c_1{}_2{F}_1(\frac{a}{4}-\frac{1}{4}\sqrt{a^2-2a-4c+1}-\frac{1}{4},\frac{a}{4}+\frac{1}{4}\sqrt{a^2-2a-4c+1}-\frac{1}{4};\frac{1}{2}-\frac{b}{2};x^2)+i^{b+1}{c}_2{x}^{b+1}{}_2{F}_1(\frac{a}{4}+\frac{b}{2}-\frac{1}{4}\sqrt{a^2-2a-4c+1}+\frac{1}{4},\frac{a}{4}+\frac{b}{2}+\frac{1}{4}\sqrt{a^2-2a-4c+1}+\frac{1}{4};\frac{b}{2}+\frac{3}{2};x^2)\}\right\}$$

Maple: cpu = 0.094 (sec), leaf count = 122 $$\{y\left(x\right)=\mathit{\_}\mathit{C}\mathit{1}{}_2\text{F}{}_1(-\frac{1}{4}+\frac{a}{4}-\frac{1}{4}\sqrt{a^2-2a-4c+1},-\frac{1}{4}+\frac{a}{4}+\frac{1}{4}\sqrt{a^2-2a-4c+1};\frac{1}{2}-\frac{b}{2};x^2)+\mathit{\_}\mathit{C}\mathit{2}{x}^{b+1}{}_2\text{F}{}_1(\frac{1}{4}+\frac{a}{4}+\frac{b}{2}+\frac{1}{4}\sqrt{a^2-2a-4c+1},\frac{1}{4}+\frac{a}{4}+\frac{b}{2}-\frac{1}{4}\sqrt{a^2-2a-4c+1};\frac{3}{2}+\frac{b}{2};x^2)\}$$