Internal problem ID [8887]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 2, linear second order
Problem number: 1308.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {x^{3} y^{\prime \prime }-x^{2} y^{\prime }+y x -\ln \relax (x )^{3}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.003 (sec). Leaf size: 36
dsolve(x^3*diff(diff(y(x),x),x)-x^2*diff(y(x),x)+x*y(x)-ln(x)^3=0,y(x), singsol=all)
\[ y \relax (x ) = x c_{2}+x \ln \relax (x ) c_{1}+\frac {2 \ln \relax (x )^{3}+6 \ln \relax (x )^{2}+9 \ln \relax (x )+6}{8 x} \]
✓ Solution by Mathematica
Time used: 0.011 (sec). Leaf size: 38
DSolve[-Log[x]^3 + x*y[x] - x^2*y'[x] + x^3*y''[x] == 0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {\log (x) (2 \log (x) (\log (x)+3)+9)+6}{8 x}+c_1 x+c_2 x \log (x) \\ \end{align*}