Internal problem ID [7214]
Book: Collection of Kovacic problems
Section: section 1
Problem number: 493.
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: 0.004 (sec). Leaf size: 42
dsolve(diff(y(x),x$2)+x*diff(y(x),x)+2*y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = c_{1} x \,{\mathrm e}^{-\frac {x^{2}}{2}}+c_{2} \left (i \sqrt {\pi }\, \sqrt {2}\, \erf \left (\frac {i \sqrt {2}\, x}{2}\right ) x \,{\mathrm e}^{-\frac {x^{2}}{2}}+2\right ) \]
✓ Solution by Mathematica
Time used: 0.005 (sec). Leaf size: 44
DSolve[y''[x]+x*y'[x]+2*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\sqrt {2} c_2 x F\left (\frac {x}{\sqrt {2}}\right )+\sqrt {2} c_1 e^{-\frac {x^2}{2}} x+c_2 \\ \end{align*}