Internal problem ID [6953]
Book: Collection of Kovacic problems
Section: section 1
Problem number: 222.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [_erf]
Solve \begin {gather*} \boxed {y^{\prime \prime }+2 x y^{\prime }+4 y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.005 (sec). Leaf size: 31
dsolve(diff(y(x),x$2)+2*x*diff(y(x),x)+4*y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = c_{1} x \,{\mathrm e}^{-x^{2}}+c_{2} \left ({\mathrm e}^{-x^{2}} \sqrt {\pi }\, \erfi \relax (x ) x -1\right ) \]
✓ Solution by Mathematica
Time used: 0.007 (sec). Leaf size: 27
DSolve[y''[x]+2*x*y'[x]+4*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -2 c_2 x F(x)+2 c_1 e^{-x^2} x+c_2 \\ \end{align*}