26.1.5 problem 1.

Internal problem ID [4245]
Book : Differential equations with applications and historial notes, George F. Simmons. Second edition. 1971
Section : Chapter 2, section 7, page 37
Problem number : 1.
Date solved : Monday, January 27, 2025 at 08:44:16 AM
CAS classification : [[_homogeneous, `class D`]]

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

✓ Solution by Maple

Time used: 0.006 (sec). Leaf size: 19

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

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

✓ Solution by Mathematica

Time used: 0.622 (sec). Leaf size: 16

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

\[ y(x)\to x \log \left (-\frac {2}{x}+c_1\right ) \]