47.2.7 problem 7

Internal problem ID [7423]
Book : Ordinary differential equations and calculus of variations. Makarets and Reshetnyak. Wold Scientific. Singapore. 1995
Section : Chapter 1. First order differential equations. Section 1.2 Homogeneous equations problems. page 12
Problem number : 7
Date solved : Monday, January 27, 2025 at 02:54:37 PM
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: 0.006 (sec). Leaf size: 12

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

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

✓ Solution by Mathematica

Time used: 0.384 (sec). Leaf size: 16

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

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