28.1.96 problem 119

Internal problem ID [4402]
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
Date solved : Monday, January 27, 2025 at 09:14:47 AM
CAS classification : [[_homogeneous, `class A`], _dAlembert]

\begin{align*} y^{\prime }&={\mathrm e}^{\frac {x y^{\prime }}{y}} \end{align*}

✓ Solution by Maple

Time used: 0.061 (sec). Leaf size: 14

dsolve(diff(y(x),x)=exp(x*diff(y(x),x)/y(x)),y(x), singsol=all)
 

\[ y \left (x \right ) = -\frac {{\mathrm e}^{-c_{1} x}}{c_{1}} \]

✓ Solution by Mathematica

Time used: 0.069 (sec). Leaf size: 21

DSolve[D[y[x],x]==Exp[x*D[y[x],x]/y[x]],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to -e^{c_1-e^{-c_1} x} \]