Internal problem ID [5755]
Book: Ordinary differential equations and calculus of variations. Makarets and Reshetnyak. Wold
Scientific. Singapore. 1995
Section: Chapter 1. First order differential equations. Section 1.2 Homogeneous equations
problems. page 12
Problem number: 7.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class A`], _dAlembert]
\[ \boxed {x y^{\prime }-y+x \,{\mathrm e}^{\frac {y}{x}}=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 12
dsolve(x*diff(y(x),x)=y(x)-x*exp(y(x)/x),y(x), singsol=all)
\[ y \left (x \right ) = -\ln \left (\ln \left (x \right )+c_{1} \right ) x \]
✓ Solution by Mathematica
Time used: 0.348 (sec). Leaf size: 16
DSolve[x*y'[x]==y[x]-x*Exp[y[x]/x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to -x \log (\log (x)-c_1) \]