Internal problem ID [7964]
Book: Collection of Kovacic problems
Section: section 1
Problem number: 487.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {\left (x^{2}+1\right ) y^{\prime \prime }+2 x y^{\prime }-2 y=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 16
dsolve((1+x^2)*diff(y(x),x$2)+2*x*diff(y(x),x)-2*y(x)=0,y(x), singsol=all)
\[ y \left (x \right ) = c_{1} x +c_{2} \left (\arctan \left (x \right ) x +1\right ) \]
✓ Solution by Mathematica
Time used: 0.021 (sec). Leaf size: 48
DSolve[(1+x^2)*y''[x]+2*x*y'[x]-2*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {1}{2} i (2 c_1 x-c_2 x \log (1-i x)+c_2 x \log (1+i x)+2 i c_2) \]