Internal problem ID [11141]
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]
\[ \boxed {x \,{\mathrm e}^{\frac {y}{x}}+y-y^{\prime } x=0} \]
✓ 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)
\[ y \left (x \right ) = \ln \left (-\frac {1}{\ln \left (x \right )+c_{1}}\right ) x \]
✓ Solution by Mathematica
Time used: 0.527 (sec). Leaf size: 18
DSolve[(x*Exp[y[x]/x]+y[x])-x*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to -x \log (-\log (x)-c_1) \]