Internal problem ID [8679]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 2, linear second order
Problem number: 1099.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {x y^{\prime \prime }-y^{\prime }+x^{3} \left ({\mathrm e}^{x^{2}}-v^{2}\right ) y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.422 (sec). Leaf size: 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), singsol=all)
\[ y \relax (x ) = c_{1} \BesselJ \left (v , {\mathrm e}^{\frac {x^{2}}{2}}\right )+c_{2} \BesselY \left (v , {\mathrm e}^{\frac {x^{2}}{2}}\right ) \]
✗ Solution by Mathematica
Time used: 0.0 (sec). Leaf size: 0
DSolve[(E^x^3 - v^2)*x^3*y[x] - y'[x] + x*y''[x] == 0,y[x],x,IncludeSingularSolutions -> True]
Not solved