Internal problem ID [7226]
Book: Collection of Kovacic problems
Section: section 1
Problem number: 506.
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 }+\left (x +1\right ) y^{\prime }+3 y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 58
dsolve((2+x)*diff(y(x),x$2)+(1+x)*diff(y(x),x)+3*y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = c_{1} {\mathrm e}^{-x} x \left (x -4\right ) \left (x +2\right )^{2}+c_{2} \left ({\mathrm e}^{-x -2} x \left (x -4\right ) \left (x +2\right )^{2} \expIntegral \left (1, -x -2\right )+x^{3}-x^{2}-10 x -6\right ) \]
✓ Solution by Mathematica
Time used: 0.16 (sec). Leaf size: 64
DSolve[(2+x)*y''[x]+(1+x)*y'[x]+3*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {e^{-x-1} \left ((x-4) x (x+2)^2 (c_2 \text {Ei}(x+2)+384 c_1)-c_2 e^{x+2} (x ((x-1) x-10)-6)\right )}{96 \sqrt {2}} \\ \end{align*}