\[ \boxed { x{\frac {{\rm d}^{2}}{{\rm d}{x}^{2}}}y \left ( x \right ) -{\frac {\rm d}{{\rm d}x}}y \left ( x \right ) +{x}^{3} \left ( {{\rm e}^{{x}^{2}}}-{v}^{2} \right ) y \left ( x \right ) =0} \]
Mathematica: cpu = 1.065635 (sec), leaf count = 36 \[ \text {DSolve}\left [x^3 \left (e^{x^3}-v^2\right ) y(x)+x y''(x)-y'(x)=0,y(x),x\right ] \]
Maple: cpu = 0.031 (sec), leaf count = 25 \[ \left \{ y \left ( x \right ) ={\it \_C1}\,{{\sl J}_{v}\left ({{\rm e}^{{ \frac {{x}^{2}}{2}}}}\right )}+{\it \_C2}\,{{\sl Y}_{v}\left ({{\rm e}^{ {\frac {{x}^{2}}{2}}}}\right )} \right \} \]