Internal problem ID [7805]
Book: Collection of Kovacic problems
Section: section 1
Problem number: 319.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {\left (x +2\right ) y^{\prime \prime }+x y^{\prime }-y=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 17
dsolve((x+2)*diff(y(x),x$2)+x*diff(y(x),x)-y(x)=0,y(x), singsol=all)
\[ y \left (x \right ) = c_{1} x +c_{2} {\mathrm e}^{-x} \left (x +4\right ) \]
✓ Solution by Mathematica
Time used: 0.126 (sec). Leaf size: 72
DSolve[(x+2)*y''[x]+x*y'[x]-y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to -\frac {2 \sqrt {\frac {2}{\pi }} e^{-x-2} \sqrt {x+2} \left (c_1 \left (e^{x+2} x+x+4\right )-i c_2 \left (\left (e^{x+2}-1\right ) x-4\right )\right )}{\sqrt {-i (x+2)}} \]