Internal problem ID [2195]
Book: Differential equations and linear algebra, Stephen W. Goode and Scott A Annin. Fourth edition,
2015
Section: Chapter 1, First-Order Differential Equations. Section 1.8, Change of Variables. page
79
Problem number: Problem 58.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class G]]
Solve \begin {gather*} \boxed {y^{\prime }-\frac {y \left (\ln \left (y x \right )-1\right )}{x}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.014 (sec). Leaf size: 14
dsolve(diff(y(x),x)=y(x)/x*(ln(x*y(x))-1),y(x), singsol=all)
\[ y \relax (x ) = \frac {{\mathrm e}^{\frac {x}{c_{1}}}}{x} \]
✓ Solution by Mathematica
Time used: 0.214 (sec). Leaf size: 24
DSolve[y'[x]==y[x]/x*(Log[x*y[x]]-1),y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {e^{e^{c_1} x}}{x} \\ y(x)\to \frac {1}{x} \\ \end{align*}