Internal problem ID [8991]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 2, linear second order
Problem number: 1412.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, _with_symmetry_[0,F(x)]]]
Solve \begin {gather*} \boxed {y^{\prime \prime }-\frac {y^{\prime }}{x \ln \relax (x )}-\ln \relax (x )^{2} y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 27
dsolve(diff(diff(y(x),x),x) = 1/x/ln(x)*diff(y(x),x)+ln(x)^2*y(x),y(x), singsol=all)
\[ y \relax (x ) = c_{1} \sinh \left (x \ln \relax (x )-x \right )+c_{2} \cosh \left (x \ln \relax (x )-x \right ) \]
✓ Solution by Mathematica
Time used: 0.009 (sec). Leaf size: 29
DSolve[y''[x] == Log[x]^2*y[x] + y'[x]/(x*Log[x]),y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to c_1 \cosh (x (\log (x)-1))+i c_2 \sinh (x (\log (x)-1)) \\ \end{align*}