4.364   ODE No. 1364

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

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

Mathematica: cpu = 0.171522 (sec), leaf count = 42 $$\left\{\{y(x)\to c_1{P}_v(x)e^{a\log (x)+b{x}^c}+c_2{Q}_v(x)e^{a\log (x)+b{x}^c}\}\right\}$$

Maple: cpu = 0.078 (sec), leaf count = 33 $$\{y\left(x\right)=\mathit{\_}\mathit{C}\mathit{1}{x}^a{\mathrm{e}}^{b{x}^c}\mathit{L}\mathit{e}\mathit{g}\mathit{e}\mathit{n}\mathit{d}\mathit{r}\mathit{e}\mathit{P}(v,x)+\mathit{\_}\mathit{C}\mathit{2}{x}^a{\mathrm{e}}^{b{x}^c}\mathit{L}\mathit{e}\mathit{g}\mathit{e}\mathit{n}\mathit{d}\mathit{r}\mathit{e}\mathit{Q}(v,x)\}$$