4.399   ODE No. 1399

$$\boxed{{\displaystyle \frac{{\mathrm{d}}^2}{\mathrm{d}{x}^2}y\left(x\right)=\frac{(3x+1)\frac{\mathrm{d}}{\mathrm{d}x}y\left(x\right)}{(1+x)(x-1)}-36\frac{{(1+x)}^{2}y\left(x\right)}{{(x-1)}^2{(3x+5)}^2}=0}}$$

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

Mathematica: cpu = 0.053507 (sec), leaf count = 72 $$\left\{\{y(x)\to c_1{e}^{\frac{1}{2}(3\log (1-x)+\log (3x+5))}+\frac{1}{2}{c}_2{e}^{\frac{1}{2}(3\log (1-x)+\log (3x+5))}(3\log (1-x)+\log (3x+5))\}\right\}$$

Maple: cpu = 0.062 (sec), leaf count = 46 $$\{y\left(x\right)=\mathit{\_}\mathit{C}\mathit{1}\sqrt{3x+5}{(x-1)}^{\frac{3}{2}}+\mathit{\_}\mathit{C}\mathit{2}\sqrt{3x+5}{(x-1)}^{\frac{3}{2}}(\ln (3x+5)+3\ln (x-1))\}$$