2.1309   ODE No. 1309

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

$$x^3{y}^{″}(x)-(x^2-1)y^{\prime }(x)+xy(x)=0$$ ✓ Mathematica : cpu = 0.0999429 (sec), leaf count = 84

$$\left\{\{y(x)\to c_2{G}_{1,2}^{2,0}(-\frac{1}{2x^2}|\begin{array}{c}1\\ -\frac{1}{2},-\frac{1}{2}\end{array})+\sqrt{2}{c}_1{e}^{\frac{1}{4x^2}}x((1-\frac{1}{2x^2})I_0\left(\frac{1}{4x^2}\right)+\frac{I_1\left(\frac{1}{4x^2}\right)}{2x^2})\}\right\}$$ ✓ Maple : cpu = 0.148 (sec), leaf count = 85

$$\{y\left(x\right)=\frac{c_1(2x^2\mathrm{BesselI}(0,\frac{1}{4x^2})-\mathrm{BesselI}(0,\frac{1}{4x^2})+\mathrm{BesselI}(1,\frac{1}{4x^2})){\mathrm{e}}^{\frac{1}{4x^2}}}{x}+\frac{c_2(2x^2\mathrm{BesselK}(0,-\frac{1}{4x^2})-\mathrm{BesselK}(0,-\frac{1}{4x^2})+\mathrm{BesselK}(1,-\frac{1}{4x^2})){\mathrm{e}}^{\frac{1}{4x^2}}}{x}\}$$