Internal problem ID [8915]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 2, linear second order
Problem number: 1336.
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 {\left (1-3 x \right ) y}{\left (x -1\right ) \left (2 x -1\right )^{2}}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.006 (sec). Leaf size: 50
dsolve(diff(diff(y(x),x),x) = -(-3*x+1)/(x-1)/(2*x-1)^2*y(x),y(x), singsol=all)
\[ y \relax (x ) = c_{1} \sqrt {2 x -1}\, \left (x -1\right )+c_{2} \left (\left (2 x -2\right ) \ln \left (x -1\right )+1+\left (-2 x +2\right ) \ln \left (2 x -1\right )\right ) \sqrt {2 x -1} \]
✓ Solution by Mathematica
Time used: 0.028 (sec). Leaf size: 45
DSolve[y''[x] == -(((1 - 3*x)*y[x])/((-1 + x)*(-1 + 2*x)^2)),y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\sqrt {1-2 x} (c_1 (x-1)+2 c_2 (x-1) (\log (x-1)-\log (2 x-1))+c_2) \\ \end{align*}