Internal problem ID [8294]
Book: Collection of Kovacic problems
Section: section 1
Problem number: 822.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {y^{\prime \prime }-y^{\prime } x -y x=0} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 54
dsolve(diff(y(x),x$2)-x*diff(y(x),x)-x*y(x)=0,y(x), singsol=all)
\[ y \left (x \right ) = c_{1} {\mathrm e}^{-x} \left (x +2\right )+c_{2} \left (i \left (x +2\right ) \operatorname {erf}\left (\frac {i \sqrt {2}\, \left (x +2\right )}{2}\right ) \sqrt {2}\, \sqrt {\pi }\, {\mathrm e}^{-2-x}+2 \,{\mathrm e}^{\frac {x \left (x +2\right )}{2}}\right ) \]
✓ Solution by Mathematica
Time used: 0.11 (sec). Leaf size: 78
DSolve[y''[x]-x*y'[x]-x*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {1}{2} e^{-x} \left (-\sqrt {2 \pi } c_2 \sqrt {(x+2)^2} \text {erfi}\left (\frac {\sqrt {(x+2)^2}}{\sqrt {2}}\right )+2 \sqrt {2} c_1 (x+2)+2 c_2 e^{\frac {1}{2} (x+2)^2}\right ) \]