Internal problem ID [1916]
Book: Differential Equations, Nelson, Folley, Coral, 3rd ed, 1964
Section: Exercis 6, page 25
Problem number: 17.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class A], _dAlembert]
Solve \begin {gather*} \boxed {{\mathrm e}^{\frac {y}{x}} x +y-y^{\prime } x=0} \end {gather*} With initial conditions \begin {align*} [y \relax (1) = 0] \end {align*}
✓ Solution by Maple
Time used: 0.063 (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: 0.356 (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*}