Internal problem ID [6778]
Book: Collection of Kovacic problems
Section: section 1
Problem number: 47.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {\left (x +2\right ) y^{\prime \prime }+y^{\prime } x +3 y=0} \]
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 71
dsolve((2+x)*diff(y(x),x$2)+x*diff(y(x),x)+3*y(x)=0,y(x), singsol=all)
\[ y \left (x \right ) = c_{1} {\mathrm e}^{-x} \left (x^{2}-6 x +4\right ) \left (x +2\right )^{3}+c_{2} \left ({\mathrm e}^{-2-x} \left (x^{2}-6 x +4\right ) \left (x +2\right )^{3} \operatorname {Ei}_{1}\left (-2-x \right )+x^{4}-x^{3}-18 x^{2}-22 x +8\right ) \]
✓ Solution by Mathematica
Time used: 0.297 (sec). Leaf size: 65
DSolve[(2+x)*y''[x]+x*y'[x]+3*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {e^{-x} ((x-6) x+4) (x+2)^3 (c_2 \operatorname {ExpIntegralEi}(x+2)+3840 c_1)+e^2 c_2 \left (x \left (x \left (-x^2+x+18\right )+22\right )-8\right )}{960 e} \\ \end{align*}