Internal problem ID [7457]
Book: Collection of Kovacic problems
Section: section 1
Problem number: 738.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [_Hermite]
Solve \begin {gather*} \boxed {y^{\prime \prime }-x y^{\prime }-3 y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.062 (sec). Leaf size: 48
dsolve(diff(y(x),x$2)-x*diff(y(x),x)-3*y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = c_{1} \left (\sqrt {\pi }\, {\mathrm e}^{\frac {x^{2}}{2}} \erf \left (\frac {x \sqrt {2}}{2}\right ) \left (x^{2}+1\right )+x \sqrt {2}\right )+c_{2} {\mathrm e}^{\frac {x^{2}}{2}} \left (x^{2}+1\right ) \]
✓ Solution by Mathematica
Time used: 0.006 (sec). Leaf size: 35
DSolve[y''[x]-x*y'[x]-3*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to c_1 H_{-3}\left (\frac {x}{\sqrt {2}}\right )+c_2 e^{\frac {x^2}{2}} \left (x^2+1\right ) \\ \end{align*}