Internal problem ID [7306]
Book: Collection of Kovacic problems
Section: section 1
Problem number: 586.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {x \left (x +1\right ) y^{\prime \prime }+\left (1-x \right ) y^{\prime }+y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.005 (sec). Leaf size: 20
dsolve(x*(1+x)*diff(y(x),x$2)+(1-x)*diff(y(x),x)+y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = c_{1} \left (x -1\right )+c_{2} \left (-4+\left (x -1\right ) \ln \relax (x )\right ) \]
✓ Solution by Mathematica
Time used: 0.02 (sec). Leaf size: 23
DSolve[x*(1+x)*y''[x]+(1-x)*y'[x]+y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to c_1 (x-1)+c_2 ((x-1) \log (x)-4) \\ \end{align*}