Internal problem ID [8907]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 2, linear second order
Problem number: 1328.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {y^{\prime \prime }-\frac {2 y}{x \left (x -1\right )^{2}}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.006 (sec). Leaf size: 32
dsolve(diff(diff(y(x),x),x) = 2/x/(x-1)^2*y(x),y(x), singsol=all)
\[ y \relax (x ) = \frac {c_{1} x}{x -1}+\frac {c_{2} \left (2 x \ln \relax (x )-x^{2}+1\right )}{x -1} \]
✓ Solution by Mathematica
Time used: 0.011 (sec). Leaf size: 31
DSolve[y''[x] == (2*y[x])/((-1 + x)^2*x),y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {-x (c_2 x+c_1)+2 c_2 x \log (x)+c_2}{x-1} \\ \end{align*}