Internal problem ID [7523]
Book: Collection of Kovacic problems
Section: section 1
Problem number: 806.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {2 x y^{\prime \prime }+\left (-2+x \right ) y^{\prime }-y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 16
dsolve(2*x*diff(y(x),x$2)+(x-2)*diff(y(x),x)-y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = c_{1} \left (x -2\right )+c_{2} {\mathrm e}^{-\frac {x}{2}} \]
✓ Solution by Mathematica
Time used: 0.027 (sec). Leaf size: 23
DSolve[2*x*y''[x]+(x-2)*y'[x]-y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to c_1 e^{-x/2}+2 c_2 (x-2) \\ \end{align*}