ODE No. 1042

$$-ny(x)+y^{″}(x)+x{y}^{\prime }(x)=0$$ ✓ Mathematica : cpu = 0.0064842 (sec), leaf count = 61

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

$$\left\{\{y(x)\to c_1{e}^{-\frac{x^2}{2}}{H}_{-n-1}\left(\frac{x}{\sqrt{2}}\right)+c_2{e}^{-\frac{x^2}{2}}{}_1{F}_1(\frac{n+1}{2};\frac{1}{2};\frac{x^2}{2})\}\right\}$$ ✓ Maple : cpu = 0.07 (sec), leaf count = 41

dsolve(diff(diff(y(x),x),x)+x*diff(y(x),x)-n*y(x)=0,y(x))
 

$$y\left(x\right)={\mathrm{e}}^{-\frac{x^2}{2}}x(\mathrm{KummerU}(\frac{n}{2}+1,\frac{3}{2},\frac{x^2}{2})c_2+\mathrm{KummerM}(\frac{n}{2}+1,\frac{3}{2},\frac{x^2}{2})c_1)$$