Internal problem ID [7886]
Book: Collection of Kovacic problems
Section: section 1
Problem number: 406.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {x^{2} y^{\prime \prime }-x \left (x +2\right ) y^{\prime }+\left (x +2\right ) y=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 13
dsolve(x^2*diff(y(x),x$2)-x*(x+2)*diff(y(x),x)+(x+2)*y(x)=0,y(x), singsol=all)
\[ y \left (x \right ) = c_{1} x +{\mathrm e}^{x} c_{2} x \]
✓ Solution by Mathematica
Time used: 0.021 (sec). Leaf size: 16
DSolve[x^2*y''[x]-x*(x+2)*y'[x]+(x+2)*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to x \left (c_2 e^x+c_1\right ) \]