Internal problem ID [6743]
Book: Collection of Kovacic problems
Section: section 1
Problem number: 9.
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 }-2 y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.063 (sec). Leaf size: 42
dsolve(diff(y(x),x$2)+x*diff(y(x),x)-2*y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = c_{1} \left (\erf \left (\frac {x \sqrt {2}}{2}\right ) \sqrt {\pi }\, \left (x^{2}+1\right )+\sqrt {2}\, {\mathrm e}^{-\frac {x^{2}}{2}} x \right )+c_{2} \left (x^{2}+1\right ) \]
✓ Solution by Mathematica
Time used: 0.005 (sec). Leaf size: 35
DSolve[y''[x]+x*y'[x]-2*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to c_1 e^{-\frac {x^2}{2}} \text {HermiteH}\left (-3,\frac {x}{\sqrt {2}}\right )+c_2 \left (x^2+1\right ) \\ \end{align*}