Internal problem ID [5321]
Book: An introduction to Ordinary Differential Equations. Earl A. Coddington. Dover. NY
1961
Section: Chapter 5. Existence and uniqueness of solutions to first order equations. Page
190
Problem number: 4(d).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class A], _dAlembert]
Solve \begin {gather*} \boxed {y^{\prime }-\frac {y+x \,{\mathrm e}^{-\frac {2 y}{x}}}{x}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.005 (sec). Leaf size: 16
dsolve(diff(y(x),x)=(y(x)+x*exp(-2*y(x)/x))/x,y(x), singsol=all)
\[ y \relax (x ) = \frac {\ln \left (2 \ln \relax (x )+2 c_{1}\right ) x}{2} \]
✓ Solution by Mathematica
Time used: 0.43 (sec). Leaf size: 18
DSolve[y'[x]==(y[x]+x*Exp[-2*y[x]/x])/x,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{2} x \log (2 (\log (x)+c_1)) \\ \end{align*}