20.4.8 problem Problem 16

Internal problem ID [3643]
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
Date solved : Monday, January 27, 2025 at 07:49:32 AM
CAS classification : [[_homogeneous, `class A`], _dAlembert]

\begin{align*} x y^{\prime }+y \ln \left (x \right )&=y \ln \left (y\right ) \end{align*}

✓ Solution by Maple

Time used: 0.017 (sec). Leaf size: 13

dsolve(x*diff(y(x),x)+y(x)*ln(x)=y(x)*ln(y(x)),y(x), singsol=all)
 

\[ y \left (x \right ) = x \,{\mathrm e}^{-c_{1} x +1} \]

✓ Solution by Mathematica

Time used: 0.225 (sec). Leaf size: 24

DSolve[x*D[y[x],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*}