Internal problem ID [7776]
Book: Collection of Kovacic problems
Section: section 1
Problem number: 289.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {\left (x^{2}+1\right ) y^{\prime \prime }-2 y^{\prime } x +2 y=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 15
dsolve((x^2+1)*diff(y(x),x$2)-2*x*diff(y(x),x)+2*y(x)=0,y(x), singsol=all)
\[ y \left (x \right ) = x c_{1} +c_{2} \left (x^{2}-1\right ) \]
✓ Solution by Mathematica
Time used: 0.042 (sec). Leaf size: 21
DSolve[(x^2+1)*y''[x]-2*x*y'[x]+2*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to c_2 x-c_1 (x-i)^2 \]