Internal problem ID [8857]
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]]
\[ \boxed {4 x^{2} y^{\prime \prime }+5 y^{\prime } x -y-\ln \left (x \right )=0} \]
✓ Solution by Maple
Time used: 0.031 (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)
\[ y \left (x \right ) = x^{-\frac {1}{8}+\frac {\sqrt {17}}{8}} c_{2} +x^{-\frac {1}{8}-\frac {\sqrt {17}}{8}} c_{1} -\ln \left (x \right )-1 \]
✓ Solution by Mathematica
Time used: 0.076 (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*}