Internal problem ID [7834]
Book: Collection of Kovacic problems
Section: section 1
Problem number: 349.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {x y^{\prime \prime }+\left (-2 x +2\right ) y^{\prime }+\left (x -2\right ) y=0} \]
✓ Solution by Maple
Time used: 0.0 (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)
\[ y \left (x \right ) = \frac {c_{1} {\mathrm e}^{x}}{x}+{\mathrm e}^{x} c_{2} \]
✓ Solution by Mathematica
Time used: 0.026 (sec). Leaf size: 19
DSolve[x*y''[x]+(2-2*x)*y'[x]+(x-2)*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {e^x (c_2 x+c_1)}{x} \]