Internal problem ID [8623]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 2, linear second order
Problem number: 1043.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [_Hermite]
Solve \begin {gather*} \boxed {y^{\prime \prime }-x y^{\prime }+2 y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.008 (sec). Leaf size: 44
dsolve(diff(diff(y(x),x),x)-x*diff(y(x),x)+2*y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = c_{1} \left (-2 x \,{\mathrm e}^{\frac {x^{2}}{2}}+\erfi \left (\frac {\sqrt {2}\, x}{2}\right ) \sqrt {\pi }\, \sqrt {2}\, \left (x -1\right ) \left (x +1\right )\right )+c_{2} \left (x^{2}-1\right ) \]
✓ Solution by Mathematica
Time used: 0.142 (sec). Leaf size: 53
DSolve[2*y[x] - x*y'[x] + y''[x] == 0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{4} \left (\left (x^2-1\right ) \left (\sqrt {2 \pi } c_2 \text {Erfi}\left (\frac {x}{\sqrt {2}}\right )+4 c_1\right )-2 c_2 e^{\frac {x^2}{2}} x\right ) \\ \end{align*}