3.1 problem Ex 1

Internal problem ID [10117]

Book: An elementary treatise on differential equations by Abraham Cohen. DC heath publishers. 1906
Section: Chapter 2, differential equations of the first order and the first degree. Article 10. Homogeneous equations. Page 15
Problem number: Ex 1.
ODE order: 1.
ODE degree: 1.

CAS Maple gives this as type [[_homogeneous, class A], _dAlembert]

Solve \begin {gather*} \boxed {x \,{\mathrm e}^{\frac {y}{x}}+y-y^{\prime } x=0} \end {gather*}

Solution by Maple

Time used: 0.0 (sec). Leaf size: 15

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

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

Solution by Mathematica

Time used: 0.358 (sec). Leaf size: 18

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

\begin{align*} y(x)\to -x \log (-\log (x)-c_1) \\ \end{align*}