Internal problem ID [3930]
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 7.13, page
61.
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-x y^{\prime }=0} \end {gather*} With initial conditions \begin {align*} [y \relax (1) = 0] \end {align*}
✓ Solution by Maple
Time used: 0.039 (sec). Leaf size: 15
dsolve([(x*exp(y(x)/x)+y(x))=x*diff(y(x),x),y(1) = 0],y(x), singsol=all)
\[ y \relax (x ) = \ln \left (-\frac {1}{\ln \relax (x )-1}\right ) x \]
✓ Solution by Mathematica
Time used: 0.349 (sec). Leaf size: 15
DSolve[{(x*Exp[y[x]/x]+y[x])==x*y'[x],y[1]==0},y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -x \log (1-\log (x)) \\ \end{align*}