Internal problem ID [8831]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 2, linear second order
Problem number: 1251.
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 (x -1\right ) y^{\prime }+y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 20
dsolve(x*(x+1)*diff(diff(y(x),x),x)-(x-1)*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: 0.021 (sec). Leaf size: 23
DSolve[y[x] - (-1 + x)*y'[x] + x*(1 + 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*}