Internal problem ID [7499]
Book: Collection of Kovacic problems
Section: section 1
Problem number: 9.
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: 0.015 (sec). Leaf size: 35
dsolve(diff(y(x),x$2)+x*diff(y(x),x)-2*y(x)=0,y(x), singsol=all)
\[ y \left (x \right ) = c_{1} \left (x^{2}+1\right )+c_{2} \left (x^{2}+1\right ) \left (\int \frac {{\mathrm e}^{-\frac {x^{2}}{2}}}{\left (x^{2}+1\right )^{2}}d x \right ) \]
✓ Solution by Mathematica
Time used: 0.022 (sec). Leaf size: 35
DSolve[y''[x]+x*y'[x]-2*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to c_1 e^{-\frac {x^2}{2}} \operatorname {HermiteH}\left (-3,\frac {x}{\sqrt {2}}\right )+c_2 \left (x^2+1\right ) \]