2.1483   ODE No. 1483

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

$$-4(\nu +x-1)y^{″}(x)+(6\nu +2x-5)y^{\prime }(x)+(1-2\nu )y(x)+2x{y}^{(3)}(x)=0$$ ✓ Mathematica : cpu = 0.146108 (sec), leaf count = 112

$$\left\{\{y(x)\to \frac{c_3{e}^{x}x\mathrm{\Gamma }(\frac{5}{2}-3\nu )(\frac{2{}_1{\tilde{F}}_1(\frac{3}{2}-3\nu ;1-2\nu ;-x)}{3(2\nu -1)x}+\frac{2}{3x\mathrm{\Gamma }(2-2\nu )})}{\mathrm{\Gamma }(\frac{3}{2}-\nu )}+c_2{e}^x{G}_{2,3}^{2,1}\left(x|\begin{array}{c}1,3\nu -\frac{1}{2}\\ 1,2\nu ,0\end{array}\right)+c_1{e}^x\}\right\}$$

✓ Maple : cpu = 0.267 (sec), leaf count = 37

$$\{y\left(x\right)=\mathit{\_}\mathit{C}\mathit{1}{\mathrm{e}}^x+\mathit{\_}\mathit{C}\mathit{2}{\mathrm{e}}^{\frac{x}{2}}{x}^{\nu }{\mathit{I}}_{\nu }\left(\frac{x}{2}\right)+\mathit{\_}\mathit{C}\mathit{3}{\mathrm{e}}^{\frac{x}{2}}{x}^{\nu }{\mathit{K}}_{\nu }\left(\frac{x}{2}\right)\}$$