29.15.33 problem 441

Internal problem ID [5039]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 15
Problem number : 441
Date solved : Monday, January 27, 2025 at 10:05:13 AM
CAS classification : [[_homogeneous, `class A`], _dAlembert]

\begin{align*} \left (x -y\right ) y^{\prime }&=\left ({\mathrm e}^{-\frac {x}{y}}+1\right ) y \end{align*}

✓ Solution by Maple

Time used: 0.061 (sec). Leaf size: 20

dsolve((x-y(x))*diff(y(x),x) = (exp(-x/y(x))+1)*y(x),y(x), singsol=all)
 

\[ y \left (x \right ) = -\frac {x}{\operatorname {LambertW}\left (\frac {x c_{1}}{c_{1} x -1}\right )} \]

✓ Solution by Mathematica

Time used: 1.306 (sec). Leaf size: 34

DSolve[(x-y[x])D[y[x],x]==(Exp[-x/y[x]]+1)y[x],y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to -\frac {x}{W\left (\frac {x}{x-e^{c_1}}\right )} \\ y(x)\to -\frac {x}{W(1)} \\ \end{align*}