Internal problem ID [7171]
Book: Collection of Kovacic problems
Section: section 1
Problem number: 448.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {x^{2} y^{\prime \prime }+2 x \left (x -1\right ) y^{\prime }+\left (x^{2}-2 x +2\right ) y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 21
dsolve(x^2*diff(y(x),x$2)+2*x*(x-1)*diff(y(x),x)+(x^2-2*x+2)*y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = c_{1} x \,{\mathrm e}^{-x}+c_{2} x^{2} {\mathrm e}^{-x} \]
✓ Solution by Mathematica
Time used: 0.015 (sec). Leaf size: 19
DSolve[x^2*y''[x]+2*x*(x-1)*y'[x]+(x^2-2*x+2)*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to e^{-x} x (c_2 x+c_1) \\ \end{align*}