50.5.5 problem 1(e)

Internal problem ID [7875]
Book : Differential Equations: Theory, Technique, and Practice by George Simmons, Steven Krantz. McGraw-Hill NY. 2007. 1st Edition.
Section : Chapter 1. What is a differential equation. Section 1.7. Homogeneous Equations. Page 28
Problem number : 1(e)
Date solved : Monday, January 27, 2025 at 03:29:39 PM
CAS classification : [[_homogeneous, `class A`], _dAlembert]

\begin{align*} x y^{\prime }&=y+2 x \,{\mathrm e}^{-\frac {y}{x}} \end{align*}

✓ Solution by Maple

Time used: 0.006 (sec). Leaf size: 14

dsolve(x*diff(y(x),x)=y(x)+2*x*exp(-y(x)/x),y(x), singsol=all)
 

\[ y = \left (\ln \left (2\right )+\ln \left (\ln \left (x \right )+c_{1} \right )\right ) x \]

✓ Solution by Mathematica

Time used: 0.422 (sec). Leaf size: 15

DSolve[x*D[y[x],x]==y[x]+2*x*Exp[-y[x]/x],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to x \log (2 \log (x)+c_1) \]