Internal problem ID [7087]
Book: Collection of Kovacic problems
Section: section 1
Problem number: 358.
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 (1-2 x \right ) y^{\prime }+\left (x -1\right ) y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.004 (sec). Leaf size: 15
dsolve(x*diff(y(x),x$2)+(1-2*x)*diff(y(x),x)+(x-1)*y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = c_{1} {\mathrm e}^{x}+c_{2} {\mathrm e}^{x} \ln \relax (x ) \]
✓ Solution by Mathematica
Time used: 0.007 (sec). Leaf size: 17
DSolve[x*y''[x]+(1-2*x)*y'[x]+(x-1)*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to e^x (c_2 \log (x)+c_1) \\ \end{align*}