Internal problem ID [7632]
Book: Collection of Kovacic problems
Section: section 1
Problem number: 144.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {x^{2} \left (x^{2}+1\right ) y^{\prime \prime }-x \left (-2 x^{2}+1\right ) y^{\prime }+y=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 33
dsolve(x^2*(1+x^2)*diff(y(x),x$2)-x*(1-2*x^2)*diff(y(x),x)+y(x)=0,y(x), singsol=all)
\[ y \left (x \right ) = \frac {c_{1} x}{\sqrt {x^{2}+1}}+\frac {c_{2} x \,\operatorname {arctanh}\left (\frac {1}{\sqrt {x^{2}+1}}\right )}{\sqrt {x^{2}+1}} \]
✓ Solution by Mathematica
Time used: 0.085 (sec). Leaf size: 33
DSolve[x^2*(1+x^2)*y''[x]-x*(1-2*x^2)*y'[x]+y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {x \left (c_1-c_2 \text {arctanh}\left (\sqrt {x^2+1}\right )\right )}{\sqrt {x^2+1}} \]