76.5.10 problem 10

Internal problem ID [17430]
Book : Differential equations. An introduction to modern methods and applications. James Brannan, William E. Boyce. Third edition. Wiley 2015
Section : Chapter 2. First order differential equations. Section 2.7 (Substitution Methods). Problems at page 108
Problem number : 10
Date solved : Tuesday, January 28, 2025 at 10:09:23 AM
CAS classification : [[_homogeneous, `class A`], _dAlembert]

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

✓ Solution by Maple

Time used: 0.511 (sec). Leaf size: 19

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

\[ y = \frac {x}{\operatorname {RootOf}\left (-\textit {\_Z} \,{\mathrm e}^{{\mathrm e}^{\textit {\_Z}}}+c_{1} x \right )} \]

✓ Solution by Mathematica

Time used: 0.221 (sec). Leaf size: 29

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

\[ \text {Solve}\left [\log \left (\frac {y(x)}{x}\right )-e^{\frac {x}{y(x)}}=-\log (x)+c_1,y(x)\right ] \]