Internal problem ID [2732]
Book: Differential equations for engineers by Wei-Chau XIE, Cambridge Press 2010
Section: Chapter 2. First-Order and Simple Higher-Order Differential Equations. Page
78
Problem number: 119.
ODE order: 1.
ODE degree: -1.
CAS Maple gives this as type [[_homogeneous, class A], _dAlembert]
Solve \begin {gather*} \boxed {y^{\prime }-{\mathrm e}^{\frac {x y^{\prime }}{y}}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.031 (sec). Leaf size: 15
dsolve(diff(y(x),x)=exp(x*diff(y(x),x)/y(x)),y(x), singsol=all)
\[ y \relax (x ) = -\frac {{\mathrm e}^{-c_{1} x}}{c_{1}} \]
✓ Solution by Mathematica
Time used: 0.058 (sec). Leaf size: 21
DSolve[y'[x]==Exp[x*y'[x]/y[x]],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -e^{c_1-e^{-c_1} x} \\ \end{align*}