Internal problem ID [8213]
Book: Collection of Kovacic problems
Section: section 1
Problem number: 738.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [_Hermite]
\[ \boxed {y^{\prime \prime }-y^{\prime } x -3 y=0} \]
✓ Solution by Maple
Time used: 0.047 (sec). Leaf size: 48
dsolve(diff(y(x),x$2)-x*diff(y(x),x)-3*y(x)=0,y(x), singsol=all)
\[ y \left (x \right ) = c_{1} \left (\sqrt {\pi }\, \left (x^{2}+1\right ) {\mathrm e}^{\frac {x^{2}}{2}} \operatorname {erf}\left (\frac {\sqrt {2}\, x}{2}\right )+\sqrt {2}\, x \right )+c_{2} {\mathrm e}^{\frac {x^{2}}{2}} \left (x^{2}+1\right ) \]
✓ Solution by Mathematica
Time used: 0.02 (sec). Leaf size: 35
DSolve[y''[x]-x*y'[x]-3*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to c_1 \operatorname {HermiteH}\left (-3,\frac {x}{\sqrt {2}}\right )+c_2 e^{\frac {x^2}{2}} \left (x^2+1\right ) \]