Internal problem ID [8205]
Book: Collection of Kovacic problems
Section: section 1
Problem number: 730.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {x \left (x +1\right ) y^{\prime \prime }-y^{\prime } \left (x -1\right )+y=0} \]
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 20
dsolve(x*(x+1)*diff(y(x),x$2)-(x-1)*diff(y(x),x)+y(x)=0,y(x), singsol=all)
\[ y \left (x \right ) = c_{1} \left (x -1\right )+c_{2} \left (-4+\left (x -1\right ) \ln \left (x \right )\right ) \]
✓ Solution by Mathematica
Time used: 0.045 (sec). Leaf size: 23
DSolve[x*(x+1)*y''[x]-(x-1)*y'[x]+y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to c_1 (x-1)+c_2 ((x-1) \log (x)-4) \]