28.1.11 problem 11

Internal problem ID [4317]
Book : Differential equations for engineers by Wei-Chau XIE, Cambridge Press 2010
Section : Chapter 2. First-Order and Simple Higher-Order Differential Equations. Page 78
Problem number : 11
Date solved : Monday, January 27, 2025 at 09:02:05 AM
CAS classification : [[_homogeneous, `class A`], _dAlembert]

\begin{align*} x y^{\prime }&=y \left (1+\ln \left (y\right )-\ln \left (x \right )\right ) \end{align*}

✓ Solution by Maple

Time used: 0.017 (sec). Leaf size: 11

dsolve(x*diff(y(x),x)=y(x)*(1+ln(y(x))-ln(x)),y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.208 (sec). Leaf size: 20

DSolve[x*D[y[x],x]==y[x]*(1+Log[y[x]]-Log[x]),y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to x e^{e^{c_1} x} \\ y(x)\to x \\ \end{align*}