Internal problem ID [7068]
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]]
Solve \begin {gather*} \boxed {y^{\prime \prime }-x^{2} y^{\prime }+y x=0} \end {gather*}
✓ Solution by Maple
Time used: 0.005 (sec). Leaf size: 48
dsolve(diff(y(x),x$2)-x^2*diff(y(x),x)+x*y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = c_{1} x +\frac {c_{2} \left (3^{\frac {1}{3}} \left (-x^{3}\right )^{\frac {2}{3}} {\mathrm e}^{\frac {x^{3}}{3}}-x^{3} \left (\Gamma \left (\frac {2}{3}\right )-\Gamma \left (\frac {2}{3}, -\frac {x^{3}}{3}\right )\right )\right )}{x^{2}} \]
✓ Solution by Mathematica
Time used: 0.029 (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 E_{\frac {4}{3}}\left (-\frac {x^3}{3}\right ) \\ \end{align*}