Internal problem ID [7388]
Book: Collection of Kovacic problems
Section: section 1
Problem number: 669.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {y^{\prime \prime }+x y^{\prime }-4 y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.03 (sec). Leaf size: 57
dsolve(diff(y(x),x$2)+x*diff(y(x),x)-4*y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = c_{1} \left ({\mathrm e}^{-\frac {x^{2}}{2}} \left (x^{2}+5\right ) \sqrt {2}\, x +\sqrt {\pi }\, \erf \left (\frac {x \sqrt {2}}{2}\right ) \left (x^{4}+6 x^{2}+3\right )\right )+c_{2} \left (x^{4}+6 x^{2}+3\right ) \]
✓ Solution by Mathematica
Time used: 0.003 (sec). Leaf size: 43
DSolve[y''[x]+x*y'[x]-4*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to c_1 e^{-\frac {x^2}{2}} H_{-5}\left (\frac {x}{\sqrt {2}}\right )+\frac {1}{3} c_2 \left (x^4+6 x^2+3\right ) \\ \end{align*}