Internal problem ID [7546]
Book: Collection of Kovacic problems
Section: section 1
Problem number: 830.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {x y^{\prime \prime }+\left (x +1\right ) y^{\prime }+2 y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 31
dsolve(x*diff(y(x), x$2) +(1+x)*diff(y(x),x)+2*y(x) = 0,y(x), singsol=all)
\[ y \relax (x ) = c_{1} \left (x -1\right ) {\mathrm e}^{-x}+c_{2} \left (1+{\mathrm e}^{-x} \left (x -1\right ) \expIntegral \left (1, -x \right )\right ) \]
✓ Solution by Mathematica
Time used: 0.043 (sec). Leaf size: 27
DSolve[x*y''[x] +(1+x)*y'[x]+2*y[x] == 0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to e^{-x} (x-1) (c_2 \operatorname {Ei}(x)+c_1)-c_2 \\ \end{align*}