ODE No. 1309

$$x^3{y}^{″}(x)-(x^2-1)y^{\prime }(x)+xy(x)=0$$ ✓ Mathematica : cpu = 0.086244 (sec), leaf count = 84

DSolve[x*y[x] - (-1 + x^2)*Derivative[1][y][x] + x^3*Derivative[2][y][x] == 0,y[x],x]
 

$$\left\{\{y(x)\to c_2{G}_{1,2}^{2,0}(-\frac{1}{2x^2}|\begin{array}{c}1\\ -\frac{1}{2},-\frac{1}{2}\end{array})+\sqrt{2}{c}_1{e}^{\frac{1}{4x^2}}x((1-\frac{1}{2x^2})I_0\left(\frac{1}{4x^2}\right)+\frac{I_1\left(\frac{1}{4x^2}\right)}{2x^2})\}\right\}$$ ✓ Maple : cpu = 0.089 (sec), leaf count = 85

dsolve(x^3*diff(diff(y(x),x),x)-(x^2-1)*diff(y(x),x)+x*y(x)=0,y(x))
 

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