Internal problem ID [7568]
Book: Collection of Kovacic problems
Section: section 2. Solution found using all possible Kovacic cases
Problem number: 8.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {\left (x^{2}-x \right ) y^{\prime \prime }-x y^{\prime }+y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 16
dsolve((x^2-x)*diff(y(x), x$2)-x*diff(y(x), x)+y(x) = 0,y(x), singsol=all)
\[ y \relax (x ) = c_{1} x +c_{2} \left (\ln \relax (x ) x +1\right ) \]
✓ Solution by Mathematica
Time used: 0.018 (sec). Leaf size: 20
DSolve[(x^2-x)*y''[x]-x*y'[x]+y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to c_1 x-c_2 (x \log (x)+1) \\ \end{align*}