Internal problem ID [8150]
Book: Collection of Kovacic problems
Section: section 1
Problem number: 675.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {x^{2} y^{\prime \prime }+x \left (-2 x +3\right ) y^{\prime }+\left (-2 x +1\right ) y=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 20
dsolve(x^2*diff(y(x),x$2)+x*(3-2*x)*diff(y(x),x)+(1-2*x)*y(x)=0,y(x), singsol=all)
\[ y \left (x \right ) = \frac {c_{1}}{x}+\frac {c_{2} \operatorname {Ei}_{1}\left (-2 x \right )}{x} \]
✓ Solution by Mathematica
Time used: 0.033 (sec). Leaf size: 19
DSolve[x^2*y''[x]+x*(3-2*x)*y'[x]+(1-2*x)*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {c_2 \operatorname {ExpIntegralEi}(2 x)+c_1}{x} \]