2.1099   ODE No. 1099

\[ x^3 \left (e^{x^3}-v^2\right ) y(x)+x y''(x)-y'(x)=0 \]

✗ Mathematica : cpu = 0.383283 (sec), leaf count = 0

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

, could not solve

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

✓ Maple : cpu = 0.085 (sec), leaf count = 25

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

\[y \left (x \right ) = c_{1} \operatorname {BesselJ}\left (v , {\mathrm e}^{\frac {x^{2}}{2}}\right )+c_{2} \operatorname {BesselY}\left (v , {\mathrm e}^{\frac {x^{2}}{2}}\right )\]