Internal problem ID [9642]
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]]
\[ \boxed {x^{3} y^{\prime \prime }-y^{\prime } x^{2}+y x=\ln \left (x \right )^{3}} \]
✓ Solution by Maple
Time used: 0.0 (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)
\[ y \left (x \right ) = c_{2} x +\ln \left (x \right ) x c_{1} +\frac {2 \ln \left (x \right )^{3}+6 \ln \left (x \right )^{2}+9 \ln \left (x \right )+6}{8 x} \]
✓ Solution by Mathematica
Time used: 0.036 (sec). Leaf size: 41
DSolve[-Log[x]^3 + x*y[x] - x^2*y'[x] + x^3*y''[x] == 0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {2 \log ^3(x)+6 \log ^2(x)+9 \log (x)+6}{8 x}+c_1 x+c_2 x \log (x) \]