2.1252   ODE No. 1252

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

$$(ax+b)y^{\prime }(x)+cy(x)+x(x+1)y^{″}(x)=0$$ ✓ Mathematica : cpu = 0.149488 (sec), leaf count = 151

$$\left\{\{y(x)\to c_2{x}^{1-b}{}_2{F}_1(\frac{a}{2}-b-\frac{1}{2}\sqrt{a^2-2a-4c+1}+\frac{1}{2},\frac{a}{2}-b+\frac{1}{2}\sqrt{a^2-2a-4c+1}+\frac{1}{2};2-b;-x)+c_1{}_2{F}_1(\frac{a}{2}-\frac{1}{2}\sqrt{a^2-2a-4c+1}-\frac{1}{2},\frac{a}{2}+\frac{1}{2}\sqrt{a^2-2a-4c+1}-\frac{1}{2};b;-x)\}\right\}$$

✓ Maple : cpu = 0.056 (sec), leaf count = 124

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