Internal problem ID [8859]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 2, linear second order
Problem number: 1279.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {4 y^{\prime \prime } x^{2}+5 x y^{\prime }-y-\ln \relax (x )=0} \end {gather*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 32
dsolve(4*x^2*diff(diff(y(x),x),x)+5*x*diff(y(x),x)-y(x)-ln(x)=0,y(x), singsol=all)
\[ y \relax (x ) = x^{-\frac {1}{8}+\frac {\sqrt {17}}{8}} c_{2}+x^{-\frac {1}{8}-\frac {\sqrt {17}}{8}} c_{1}-\ln \relax (x )-1 \]
✓ Solution by Mathematica
Time used: 0.074 (sec). Leaf size: 44
DSolve[-Log[x] - y[x] + 5*x*y'[x] + 4*x^2*y''[x] == 0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to x^{-\frac {1}{8}-\frac {\sqrt {17}}{8}} \left (c_2 x^{\frac {\sqrt {17}}{4}}+c_1\right )-\log (x)-1 \\ \end{align*}