Internal problem ID [9651]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 2, linear second order
Problem number: 1323.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, `_with_symmetry_[0,F(x)]`]]
\[ \boxed {y^{\prime \prime }+\frac {2 \left (x -2\right ) y^{\prime }}{x \left (x -1\right )}-\frac {2 \left (x +1\right ) y}{x^{2} \left (x -1\right )}=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 17
dsolve(diff(y(x),x$2) = -2/x*(x-2)/(x-1)*diff(y(x),x)+2/x^2*(x+1)/(x-1)*y(x),y(x), singsol=all)
\[ y \left (x \right ) = \frac {c_{1} +c_{2} \left (x -1\right )^{3}}{x^{2}} \]
✓ Solution by Mathematica
Time used: 0.031 (sec). Leaf size: 29
DSolve[y''[x] == -2/x*(x-2)/(x-1)*y'[x]+2/x^2*(x+1)/(x-1)*y[x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {c_2 x \left (x^2-3 x+3\right )+3 c_1}{3 x^2} \]