28.1.93 problem 115

Internal problem ID [4399]
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 : 115
Date solved : Monday, January 27, 2025 at 09:14:21 AM
CAS classification : [[_homogeneous, `class A`], _dAlembert]

\begin{align*} x y^{\prime }&=y-x \,{\mathrm e}^{\frac {y}{x}} \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 12

dsolve(x*diff(y(x),x)= y(x)-x*exp(y(x)/x),y(x), singsol=all)
 

\[ y \left (x \right ) = -\ln \left (\ln \left (x \right )+c_{1} \right ) x \]

✓ Solution by Mathematica

Time used: 0.383 (sec). Leaf size: 16

DSolve[x*D[y[x],x]== y[x]-x*Exp[y[x]/x],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to -x \log (\log (x)-c_1) \]