Internal problem ID [8136]
Book: Collection of Kovacic problems
Section: section 1
Problem number: 661.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [_erf]
\[ \boxed {y^{\prime \prime }+2 x y^{\prime }+4 y=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 36
dsolve(diff(y(x),x$2)+2*x*diff(y(x),x)+4*y(x)=0,y(x), singsol=all)
\[ y \left (x \right ) = c_{1} x \,{\mathrm e}^{-x^{2}}+c_{2} {\mathrm e}^{-x^{2}} \left (\sqrt {\pi }\, \operatorname {erfi}\left (x \right ) x -{\mathrm e}^{x^{2}}\right ) \]
✓ Solution by Mathematica
Time used: 0.041 (sec). Leaf size: 51
DSolve[y''[x]+2*x*y'[x]+4*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to e^{-x^2} \left (-\sqrt {\pi } c_2 \sqrt {x^2} \text {erfi}\left (\sqrt {x^2}\right )+c_2 e^{x^2}+2 c_1 x\right ) \]