4.339   ODE No. 1339

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

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

Mathematica: cpu = 0.263533 (sec), leaf count = 66 $$\left\{\{y(x)\to c_1{a}^{-c}{x}^{-c}{}_2{F}_1(1-c,b-c;-c-d+1;-ax)+c_2{a}^d{x}^d{}_2{F}_1(d+1,b+d;c+d+1;-ax)\}\right\}$$

Maple: cpu = 0.094 (sec), leaf count = 89 $$\{y\left(x\right)=\mathit{\_}\mathit{C}\mathit{1}{x}^d{(ax+1)}^{-b+c-d}{}_2\text{F}{}_1(c,1-b+c;1+d+c;-ax)+\mathit{\_}\mathit{C}\mathit{2}{x}^{-c}{(ax+1)}^{-b+c-d}{}_2\text{F}{}_1(-d,1-b-d;1-d-c;-ax)\}$$