Internal problem ID [8619]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 2, linear second order
Problem number: 1039.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _exact, _linear, _homogeneous]]
Solve \begin {gather*} \boxed {y^{\prime \prime }+x y^{\prime }+y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 33
dsolve(diff(diff(y(x),x),x)+x*diff(y(x),x)+y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = \erf \left (\frac {i \sqrt {2}\, x}{2}\right ) {\mathrm e}^{-\frac {x^{2}}{2}} c_{1}+c_{2} {\mathrm e}^{-\frac {x^{2}}{2}} \]
✓ Solution by Mathematica
Time used: 0.019 (sec). Leaf size: 34
DSolve[y[x] + x*y'[x] + y''[x] == 0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \sqrt {2} c_1 F\left (\frac {x}{\sqrt {2}}\right )+c_2 e^{-\frac {x^2}{2}} \\ \end{align*}