Internal problem ID [8155]
Book: Collection of Kovacic problems
Section: section 1
Problem number: 680.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {x^{2} y^{\prime \prime }+y^{\prime } x^{2}-\left (2+x \right ) y=0} \]
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 27
dsolve(x^2*diff(y(x),x$2)+x^2*diff(y(x),x)-(2+x)*y(x)=0,y(x), singsol=all)
\[ y \left (x \right ) = \frac {c_{1} {\mathrm e}^{-x}}{x}+\frac {c_{2} \left (x^{2}-2 x +2\right )}{x} \]
✓ Solution by Mathematica
Time used: 0.036 (sec). Leaf size: 31
DSolve[x^2*y''[x]+x^2*y'[x]-(2+x)*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {e^{-x} \left (c_2 e^x \left (x^2-2 x+2\right )+c_1\right )}{x} \]