Internal problem ID [8903]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 2, linear second order
Problem number: 1324.
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 (5 x -4\right ) y^{\prime }}{x \left (x -1\right )}+\frac {\left (9 x -6\right ) y}{x^{2} \left (x -1\right )}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.005 (sec). Leaf size: 21
dsolve(diff(diff(y(x),x),x) = 1/x*(5*x-4)/(x-1)*diff(y(x),x)-(9*x-6)/x^2/(x-1)*y(x),y(x), singsol=all)
\[ y \relax (x ) = c_{1} x^{3}+c_{2} x^{2} \left (x \ln \relax (x )+1\right ) \]
✓ Solution by Mathematica
Time used: 0.017 (sec). Leaf size: 24
DSolve[y''[x] == -(((-6 + 9*x)*y[x])/((-1 + x)*x^2)) + ((-4 + 5*x)*y'[x])/((-1 + x)*x),y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to x^2 (c_1 x-c_2 (x \log (x)+1)) \\ \end{align*}