32.1.9 problem First order with homogeneous Coefficients. Exercise 7.10, page 61

Internal problem ID [5779]
Book : Ordinary Differential Equations, By Tenenbaum and Pollard. Dover, NY 1963
Section : Chapter 2. Special types of differential equations of the first kind. Lesson 7
Problem number : First order with homogeneous Coefficients. Exercise 7.10, page 61
Date solved : Monday, January 27, 2025 at 01:17:19 PM
CAS classification : [[_homogeneous, `class A`], _dAlembert]

\begin{align*} 2 y \,{\mathrm e}^{\frac {x}{y}}+\left (y-2 x \,{\mathrm e}^{\frac {x}{y}}\right ) y^{\prime }&=0 \end{align*}

✓ Solution by Maple

Time used: 0.173 (sec). Leaf size: 21

dsolve(2*y(x)*exp(x/y(x))+(y(x)-2*x*exp(x/y(x)))*diff(y(x),x)=0,y(x), singsol=all)
 

\[ y \left (x \right ) = \frac {x}{\operatorname {RootOf}\left (-\textit {\_Z} \,{\mathrm e}^{-2 \,{\mathrm e}^{\textit {\_Z}}}+c_{1} x \right )} \]

✓ Solution by Mathematica

Time used: 0.235 (sec). Leaf size: 29

DSolve[2*y[x]*Exp[x/y[x]]+(y[x]-2*x*Exp[x/y[x]])*D[y[x],x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ \text {Solve}\left [-2 e^{\frac {x}{y(x)}}-\log \left (\frac {y(x)}{x}\right )=\log (x)+c_1,y(x)\right ] \]