Internal problem ID [8692]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 2, linear second order
Problem number: 1112.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {x y^{\prime \prime }-\left (x +1\right ) y^{\prime }-2 \left (x -1\right ) y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 22
dsolve(x*diff(diff(y(x),x),x)-(x+1)*diff(y(x),x)-2*(x-1)*y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = {\mathrm e}^{2 x} c_{1}+c_{2} {\mathrm e}^{-x} \left (3 x +1\right ) \]
✓ Solution by Mathematica
Time used: 0.017 (sec). Leaf size: 30
DSolve[-2*(-1 + x)*y[x] - (1 + x)*y'[x] + x*y''[x] == 0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to c_1 e^{2 x}-\frac {1}{9} c_2 e^{-x} (3 x+1) \\ \end{align*}