2.1318   ODE No. 1318

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

$$(a{x}^2+b)y^{\prime }(x)+cxy(x)+x(x^2-1)y^{″}(x)=0$$ ✓ Mathematica : cpu = 0.319698 (sec), leaf count = 146

$$\left\{\{y(x)\to c_1{}_2{F}_1(\frac{1}{4}(a-\sqrt{a^2-2a-4c+1}-1),\frac{1}{4}(a+\sqrt{a^2-2a-4c+1}-1);\frac{1-b}{2};x^2)+i^{b+1}{c}_2{x}^{b+1}{}_2{F}_1(\frac{1}{4}(a+2b-\sqrt{a^2-2a-4c+1}+1),\frac{1}{4}(a+2b+\sqrt{a^2-2a-4c+1}+1);\frac{b+3}{2};x^2)\}\right\}$$

✓ Maple : cpu = 0.141 (sec), leaf count = 122

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