Internal problem ID [7781]
Book: Collection of Kovacic problems
Section: section 1
Problem number: 294.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [_Hermite]
\[ \boxed {y^{\prime \prime }-x y^{\prime }-3 y=0} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 47
dsolve(diff(y(x),x$2)-x*diff(y(x),x)-3*y(x)=0,y(x), singsol=all)
\[ y \left (x \right ) = c_{1} {\mathrm e}^{\frac {x^{2}}{2}} \left (x^{2}+1\right )+c_{2} {\mathrm e}^{\frac {x^{2}}{2}} \left (x^{2}+1\right ) \left (\int \frac {{\mathrm e}^{-\frac {x^{2}}{2}}}{\left (x^{2}+1\right )^{2}}d x \right ) \]
✓ Solution by Mathematica
Time used: 0.019 (sec). Leaf size: 35
DSolve[y''[x]-x*y'[x]-3*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to c_1 \operatorname {HermiteH}\left (-3,\frac {x}{\sqrt {2}}\right )+c_2 e^{\frac {x^2}{2}} \left (x^2+1\right ) \]