Internal problem ID [7177]
Book: Collection of Kovacic problems
Section: section 1
Problem number: 454.
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 (2-2 x \right ) y^{\prime }+\left (x -2\right ) y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.003 (sec). Leaf size: 16
dsolve(x*diff(y(x),x$2)+(2-2*x)*diff(y(x),x)+(x-2)*y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = c_{1} {\mathrm e}^{x}+\frac {c_{2} {\mathrm e}^{x}}{x} \]
✓ Solution by Mathematica
Time used: 0.006 (sec). Leaf size: 19
DSolve[x*y''[x]+(2-2*x)*y'[x]+(x-2)*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {e^x (c_2 x+c_1)}{x} \\ \end{align*}