Internal problem ID [8214]
Book: Collection of Kovacic problems
Section: section 1
Problem number: 739.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {\left (x^{2}+1\right ) y^{\prime \prime }-x y^{\prime }+y=0} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 24
dsolve((1+x^2)*diff(y(x),x$2)-x*diff(y(x),x)+y(x)=0,y(x), singsol=all)
\[ y \left (x \right ) = c_{1} x +c_{2} \left (\operatorname {arcsinh}\left (x \right ) x -\sqrt {x^{2}+1}\right ) \]
✓ Solution by Mathematica
Time used: 0.049 (sec). Leaf size: 42
DSolve[(1+x^2)*y''[x]-x*y'[x]+y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to -c_2 \sqrt {x^2+1}-c_2 x \log \left (\sqrt {x^2+1}-x\right )+c_1 x \]