2.1339   ODE No. 1339

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

$$y^{″}(x)=-\frac{y^{\prime }(x)(a(b+2)x^2+x(c-d+1))}{x^2(ax+1)}-\frac{y(x)(abx-cd)}{x^2(ax+1)}$$ ✓ Mathematica : cpu = 0.272089 (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 = 0.142 (sec), leaf count = 76

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