78.3.5 problem 1 (e)

Internal problem ID [18108]
Book : DIFFERENTIAL EQUATIONS WITH APPLICATIONS AND HISTORICAL NOTES by George F. Simmons. 3rd edition. 2017. CRC press, Boca Raton FL.
Section : Chapter 2. First order equations. Section 7 (Homogeneous Equations). Problems at page 67
Problem number : 1 (e)
Date solved : Tuesday, January 28, 2025 at 11:27:59 AM
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: 0.004 (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: 0.408 (sec). Leaf size: 15

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

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