Internal problem ID [8866]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 2, linear second order
Problem number: 1286.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _exact, _linear, _nonhomogeneous]]
Solve \begin {gather*} \boxed {\left (3 x -1\right )^{2} y^{\prime \prime }+3 \left (3 x -1\right ) y^{\prime }-9 y-\ln \left (3 x -1\right )^{2}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 32
dsolve((3*x-1)^2*diff(diff(y(x),x),x)+3*(3*x-1)*diff(y(x),x)-9*y(x)-ln(3*x-1)^2=0,y(x), singsol=all)
\[ y \relax (x ) = \frac {c_{1}}{3 x -1}+\left (3 x -1\right ) c_{2}-\frac {\ln \left (3 x -1\right )^{2}}{9}-\frac {2}{9} \]
✓ Solution by Mathematica
Time used: 0.061 (sec). Leaf size: 74
DSolve[-Log[-1 + 3*x]^2 - 9*y[x] + 3*(-1 + 3*x)*y'[x] + (-1 + 3*x)^2*y''[x] == 0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {(2-6 x) \log ^2(3 x-1)+2 \log (3 x-1)-2 \log (1-3 x)-3 x (9 c_1 (3 x-2)+9 i c_2 (3 x-2)+4)+2-18 c_1}{54 x-18} \\ \end{align*}