2.1258   ODE No. 1258

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

$$(ax+b)y^{\prime }(x)+cy(x)+(x-1)x{y}^{″}(x)=0$$ ✓ Mathematica : cpu = 0.164758 (sec), leaf count = 146

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

✓ Maple : cpu = 0.054 (sec), leaf count = 110

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