Internal problem ID [7750]
Book: Collection of Kovacic problems
Section: section 1
Problem number: 263.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {x^{2} y^{\prime \prime }+x^{2} y^{\prime }+\left (x -2\right ) y=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 27
dsolve(x^2*diff(y(x),x$2)+x^2*diff(y(x),x)+(x-2)*y(x)=0,y(x), singsol=all)
\[ y \left (x \right ) = \frac {c_{1}}{x}+\frac {c_{2} {\mathrm e}^{-x} \left (x^{2}+2 x +2\right )}{x} \]
✓ Solution by Mathematica
Time used: 0.036 (sec). Leaf size: 29
DSolve[x^2*y''[x]+x^2*y'[x]+(x-2)*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {c_1-c_2 e^{-x} \left (x^2+2 x+2\right )}{x} \]