ODE No. 1161

$$(-a-x)y(x)+x^2{y}^{″}(x)+x{y}^{\prime }(x)=0$$ ✓ Mathematica : cpu = 0.0355606 (sec), leaf count = 78

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

$$\left\{\{y(x)\to (-1{)}^{-\sqrt{a}}{c}_1\mathrm{\Gamma }(1-2\sqrt{a})I_{-2\sqrt{a}}\left(2\sqrt{x}\right)+(-1{)}^{\sqrt{a}}{c}_2\mathrm{\Gamma }(2\sqrt{a}+1)I_{2\sqrt{a}}\left(2\sqrt{x}\right)\}\right\}$$ ✓ Maple : cpu = 0.012 (sec), leaf count = 31

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

$$y\left(x\right)=c_1\mathrm{BesselI}(2\sqrt{a},2\sqrt{x})+c_2\mathrm{BesselK}(2\sqrt{a},2\sqrt{x})$$