Internal problem ID [8990]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 2, linear second order
Problem number: 1413.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {y^{\prime \prime }-\frac {y^{\prime }}{x \left (\ln \left (x \right )-1\right )}+\frac {y}{x^{2} \left (\ln \left (x \right )-1\right )}=0} \]
✓ Solution by Maple
Time used: 0.109 (sec). Leaf size: 12
dsolve(diff(diff(y(x),x),x) = 1/x/(ln(x)-1)*diff(y(x),x)-1/x^2/(ln(x)-1)*y(x),y(x), singsol=all)
\[ y \left (x \right ) = x c_{1} +c_{2} \ln \left (x \right ) \]
✓ Solution by Mathematica
Time used: 0.028 (sec). Leaf size: 16
DSolve[y''[x] == -(y[x]/(x^2*(-1 + Log[x]))) + y'[x]/(x*(-1 + Log[x])),y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to c_1 x-c_2 \log (x) \\ \end{align*}