Internal problem ID [7970]
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]]
\[ \boxed {y^{\prime \prime }+x y^{\prime }+2 y=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 50
dsolve(diff(y(x),x$2)+x*diff(y(x),x)+2*y(x)=0,y(x), singsol=all)
\[ y \left (x \right ) = c_{1} x \,{\mathrm e}^{-\frac {x^{2}}{2}}-\frac {c_{2} {\mathrm e}^{-\frac {x^{2}}{2}} \left (i \sqrt {\pi }\, \sqrt {2}\, \operatorname {erf}\left (\frac {i \sqrt {2}\, x}{2}\right ) x +2 \,{\mathrm e}^{\frac {x^{2}}{2}}\right )}{2} \]
✓ Solution by Mathematica
Time used: 0.052 (sec). Leaf size: 69
DSolve[y''[x]+x*y'[x]+2*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to -\sqrt {\frac {\pi }{2}} c_2 e^{-\frac {x^2}{2}} \sqrt {x^2} \text {erfi}\left (\frac {\sqrt {x^2}}{\sqrt {2}}\right )+\sqrt {2} c_1 e^{-\frac {x^2}{2}} x+c_2 \]