Internal problem ID [9429]
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]]
\[ \boxed {y^{\prime \prime } x -y^{\prime }+x^{3} \left ({\mathrm e}^{x^{2}}-v^{2}\right ) y=0} \]
✓ Solution by Maple
Time used: 0.109 (sec). Leaf size: 25
dsolve(x*diff(y(x),x$2)-diff(y(x),x)+x^3*(exp(x^2)-v^2)*y(x)=0,y(x), singsol=all)
\[ y \left (x \right ) = c_{1} \operatorname {BesselJ}\left (v , {\mathrm e}^{\frac {x^{2}}{2}}\right )+c_{2} \operatorname {BesselY}\left (v , {\mathrm e}^{\frac {x^{2}}{2}}\right ) \]
✓ Solution by Mathematica
Time used: 1.118 (sec). Leaf size: 46
DSolve[x*y''[x]-y'[x]+x^3*(Exp[x^2]-v^2)*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to c_1 \operatorname {Gamma}(1-v) \operatorname {BesselJ}\left (-v,\sqrt {e^{x^2}}\right )+c_2 \operatorname {Gamma}(v+1) \operatorname {BesselJ}\left (v,\sqrt {e^{x^2}}\right ) \]