Internal problem ID [2672]
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 16.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class A`], _dAlembert]
\[ \boxed {x y^{\prime }+y \ln \left (x \right )-\ln \left (y\right ) y=0} \]
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 16
dsolve(x*diff(y(x),x)+y(x)*ln(x)=y(x)*ln(y(x)),y(x), singsol=all)
\[ y \left (x \right ) = x \,{\mathrm e}^{-c_{1} x} {\mathrm e} \]
✓ Solution by Mathematica
Time used: 0.257 (sec). Leaf size: 24
DSolve[x*y'[x]+y[x]*Log[x]==y[x]*Log[y[x]],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to x e^{1+e^{c_1} x} y(x)\to e x \end{align*}