ODE No. 1319

$$x(x^2+2)y^{″}(x)-y^{\prime }(x)-6xy(x)=0$$ ✓ Mathematica : cpu = 0.0462461 (sec), leaf count = 60

DSolve[-6*x*y[x] - Derivative[1][y][x] + x*(2 + x^2)*Derivative[2][y][x] == 0,y[x],x]
 

$$\left\{\{y(x)\to c_1{x}^{3/2}{(x^2+2)}^{3/4}-\frac{c_2{(x^2+2)}^{3/4}{}_2{F}_1(-\frac{3}{4},\frac{7}{4};\frac{1}{4};-\frac{x^2}{2})}{32^{3/4}}\}\right\}$$ ✓ Maple : cpu = 0.09 (sec), leaf count = 31

dsolve(x*(x^2+2)*diff(diff(y(x),x),x)-diff(y(x),x)-6*x*y(x)=0,y(x))
 

$$y\left(x\right)={(x^2+2)}^{\frac{3}{4}}(x^{\frac{3}{2}}{c}_1+\mathrm{hypergeom}([-\frac{3}{4},\frac{7}{4}],\left[\frac{1}{4}\right],-\frac{x^2}{2})c_2)$$