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 : Tuesday, March 04, 2025 at 06:39:51 PM
CAS classification : [[_homogeneous, `class A`], _dAlembert]

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

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

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

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

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

ode=D[y[x],x]==Exp[x*D[y[x],x]/y[x]]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

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

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-exp(x*Derivative(y(x), x)/y(x)) + Derivative(y(x), x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

NotImplementedError : multiple generators [_X0, exp(_X0*x/y(x))] 
No algorithms are implemented to solve equation _X0 - exp(_X0*x/y(x))