Internal problem ID [7457]
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]]
\[ \boxed {\left (x^{2}+1\right ) y^{\prime \prime }-y^{\prime } x +y=0} \]
✓ Solution by Maple
Time used: 0.0 (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)
\[ y \left (x \right ) = x c_{1} +c_{2} \left (\operatorname {arcsinh}\left (x \right ) x -\sqrt {x^{2}+1}\right ) \]
✓ Solution by Mathematica
Time used: 0.016 (sec). Leaf size: 29
DSolve[(1+x^2)*y''[x]-x*y'[x]+y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to c_2 x \text {arcsinh}(x)-c_2 \sqrt {x^2+1}+c_1 x \\ \end{align*}