Internal problem ID [2961]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 8
Problem number: 213.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class A], _dAlembert]
Solve \begin {gather*} \boxed {y^{\prime } x -{\mathrm e}^{\frac {y}{x}} x -y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.003 (sec). Leaf size: 15
dsolve(x*diff(y(x),x) = y(x)+x*exp(y(x)/x),y(x), singsol=all)
\[ y \relax (x ) = \ln \left (-\frac {1}{\ln \relax (x )+c_{1}}\right ) x \]
✓ Solution by Mathematica
Time used: 0.325 (sec). Leaf size: 18
DSolve[x y'[x]==y[x]+x Exp[y[x]/x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -x \log (-\log (x)-c_1) \\ \end{align*}