Internal problem ID [7067]
Book: Collection of Kovacic problems
Section: section 1
Problem number: 339.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {y^{\prime \prime }-y^{\prime } x^{2}+y x=0} \]
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 52
dsolve(diff(y(x),x$2)-x^2*diff(y(x),x)+x*y(x)=0,y(x), singsol=all)
\[ y \left (x \right ) = x c_{1} +c_{2} \left (6 \left (-x^{3}\right )^{\frac {1}{3}} 3^{\frac {2}{3}} \Gamma \left (\frac {2}{3}\right )-6 \left (-x^{3}\right )^{\frac {1}{3}} 3^{\frac {2}{3}} \Gamma \left (\frac {2}{3}, -\frac {x^{3}}{3}\right )+18 \,{\mathrm e}^{\frac {x^{3}}{3}}\right ) \]
✓ Solution by Mathematica
Time used: 0.026 (sec). Leaf size: 27
DSolve[y''[x]-x^2*y'[x]+x*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to c_1 x-\frac {1}{3} c_2 \operatorname {ExpIntegralE}\left (\frac {4}{3},-\frac {x^3}{3}\right ) \\ \end{align*}