Internal problem ID [7533]
Book: Collection of Kovacic problems
Section: section 1
Problem number: 817.
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 y^{\prime }-y x=0} \end {gather*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 54
dsolve(diff(y(x),x$2)-x*diff(y(x),x)-x*y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = c_{1} {\mathrm e}^{-x} \left (x +2\right )+c_{2} \left (i \sqrt {2}\, \sqrt {\pi }\, \left (x +2\right ) \erf \left (\frac {i \sqrt {2}\, \left (x +2\right )}{2}\right ) {\mathrm e}^{-x -2}+2 \,{\mathrm e}^{\frac {x \left (x +2\right )}{2}}\right ) \]
✓ Solution by Mathematica
Time used: 0.014 (sec). Leaf size: 63
DSolve[y''[x]-x*y'[x]-x*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{2} e^{-x} \left (\sqrt {2} (x+2) \left (2 c_1-\sqrt {\pi } c_2 \text {Erfi}\left (\frac {x+2}{\sqrt {2}}\right )\right )+2 c_2 e^{\frac {1}{2} (x+2)^2}\right ) \\ \end{align*}