Internal problem ID [7804]
Book: Collection of Kovacic problems
Section: section 1
Problem number: 318.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [_Hermite]
\[ \boxed {y^{\prime \prime }-x y^{\prime }+2 y=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 38
dsolve(diff(y(x),x$2)-x*diff(y(x),x)+2*y(x)=0,y(x), singsol=all)
\[ y \left (x \right ) = c_{1} \left (x^{2}-1\right )+c_{2} \left (x^{2}-1\right ) \left (\int \frac {{\mathrm e}^{\frac {x^{2}}{2}}}{\left (x -1\right )^{2} \left (x +1\right )^{2}}d x \right ) \]
✓ Solution by Mathematica
Time used: 0.114 (sec). Leaf size: 54
DSolve[y''[x]-x*y'[x]+2*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {1}{4} c_2 \left (\sqrt {2 \pi } \left (x^2-1\right ) \text {erfi}\left (\frac {x}{\sqrt {2}}\right )-2 e^{\frac {x^2}{2}} x\right )+c_1 \left (x^2-1\right ) \]