Internal problem ID [5076]
Book: Ordinary differential equations and calculus of variations. Makarets and Reshetnyak. Wold
Scientific. Singapore. 1995
Section: Chapter 2. Linear homogeneous equations. Section 2.3.4 problems. page 104
Problem number: 8.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {x^{2} \left (\ln \relax (x )-1\right ) y^{\prime \prime }-x y^{\prime }+y-x \left (1-\ln \relax (x )\right )^{2}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.047 (sec). Leaf size: 26
dsolve(x^2*(ln(x)-1)*diff(y(x),x$2)-x*diff(y(x),x)+y(x)=x*(1-ln(x))^2,y(x), singsol=all)
\[ y \relax (x ) = \left (\frac {\ln \relax (x )^{2}}{2}-\frac {c_{1} \ln \relax (x )}{x}-\ln \relax (x )+c_{2}\right ) x \]
✓ Solution by Mathematica
Time used: 0.062 (sec). Leaf size: 27
DSolve[x^2*(Log[x]-1)*y''[x]-x*y'[x]+y[x]==x*(1-Log[x])^2,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{2} x \log ^2(x)+c_1 x-(x+c_2) \log (x) \\ \end{align*}