Internal problem ID [7178]
Book: Collection of Kovacic problems
Section: section 1
Problem number: 455.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_Emden, _Fowler], [_2nd_order, _linear, _with_symmetry_[0,F(x)]]]
Solve \begin {gather*} \boxed {x^{2} y^{\prime \prime }-2 x y^{\prime }+2 y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.003 (sec). Leaf size: 13
dsolve(x^2*diff(y(x),x$2)-2*x*diff(y(x),x)+2*y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = c_{1} x^{2}+c_{2} x \]
✓ Solution by Mathematica
Time used: 0.003 (sec). Leaf size: 14
DSolve[x^2*y''[x]-2*x*y'[x]+2*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to x (c_2 x+c_1) \\ \end{align*}