Internal problem ID [7481]
Book: Collection of Kovacic problems
Section: section 1
Problem number: 763.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {\left (x +2\right ) y^{\prime \prime }+x y^{\prime }-y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.004 (sec). Leaf size: 17
dsolve((x+2)*diff(y(x),x$2)+x*diff(y(x),x)-y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = c_{1} x +c_{2} {\mathrm e}^{-x} \left (x +4\right ) \]
✓ Solution by Mathematica
Time used: 0.01 (sec). Leaf size: 71
DSolve[(x+2)*y''[x]+x*y'[x]-y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {2 \sqrt {\frac {2}{\pi }} e^{-x-2} \sqrt {x+2} \left ((c_1-i c_2) e^{x+2} x+(c_1+i c_2) (x+4)\right )}{\sqrt {-i (x+2)}} \\ \end{align*}