Internal problem ID [7445]
Book: Collection of Kovacic problems
Section: section 1
Problem number: 726.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {x^{2} \left (-x +2\right ) y^{\prime \prime }+2 x y^{\prime }-2 y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 16
dsolve(x^2*(2-x)*diff(y(x),x$2)+2*x*diff(y(x),x)-2*y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = c_{1} x +\frac {c_{2} \left (x -1\right )}{x} \]
✓ Solution by Mathematica
Time used: 0.028 (sec). Leaf size: 24
DSolve[x^2*(2-x)*y''[x]+2*x*y'[x]-2*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {c_1 (x-2)^2+c_2 (x-1)}{x} \\ \end{align*}