Internal problem ID [6982]
Book: Collection of Kovacic problems
Section: section 1
Problem number: 251.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {x^{2} y^{\prime \prime }+2 x \left (x +2\right ) y^{\prime }+2 \left (x +1\right ) y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.003 (sec). Leaf size: 28
dsolve(x^2*diff(y(x),x$2)+2*x*(2+x)*diff(y(x),x)+2*(1+x)*y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = \frac {c_{1}}{x}+\frac {c_{2} \left (-2 \expIntegral \left (1, 2 x \right ) x +{\mathrm e}^{-2 x}\right )}{x^{2}} \]
✓ Solution by Mathematica
Time used: 0.027 (sec). Leaf size: 32
DSolve[x^2*y''[x]+2*x*(2+x)*y'[x]+2*(1+x)*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {-2 c_2 x \operatorname {Ei}(-2 x)+c_1 x-c_2 e^{-2 x}}{x^2} \\ \end{align*}