Internal problem ID [6968]
Book: Collection of Kovacic problems
Section: section 1
Problem number: 238.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {x^{2} y^{\prime \prime }+x \left (3-x \right ) y^{\prime }+y=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 30
dsolve(x^2*diff(y(x),x$2)+x*(3-x)*diff(y(x),x)+y(x)=0,y(x), singsol=all)
\[ y \left (x \right ) = \frac {c_{1} \left (x -1\right )}{x}+\frac {c_{2} \left (\left (x -1\right ) \operatorname {Ei}_{1}\left (-x \right )+{\mathrm e}^{x}\right )}{x} \]
✓ Solution by Mathematica
Time used: 0.104 (sec). Leaf size: 29
DSolve[x^2*y''[x]+x*(3-x)*y'[x]+y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {(x-1) (c_2 \operatorname {ExpIntegralEi}(x)+c_1)-c_2 e^x}{x} \\ \end{align*}