Internal problem ID [8902]
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)]]]
Solve \begin {gather*} \boxed {y^{\prime \prime }+\frac {2 \left (-2+x \right ) y^{\prime }}{x \left (x -1\right )}-\frac {2 \left (x +1\right ) y}{x^{2} \left (x -1\right )}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 20
dsolve(diff(diff(y(x),x),x) = -2/x*(x-2)/(x-1)*diff(y(x),x)+2/x^2*(x+1)/(x-1)*y(x),y(x), singsol=all)
\[ y \relax (x ) = \frac {c_{1}}{x^{2}}+\frac {c_{2} \left (x -1\right )^{3}}{x^{2}} \]
✗ Solution by Mathematica
Time used: 0.0 (sec). Leaf size: 0
DSolve[y''[x] == (2*(1 + x)*y[x])/((-1 + x)*x) - (2*(-2 + x)*y'[x])/((-1 + x)*x),y[x],x,IncludeSingularSolutions -> True]
Not solved