28.1.100 problem 123

Internal problem ID [4406]
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 : 123
Date solved : Sunday, March 30, 2025 at 03:17:46 AM
CAS classification : [[_1st_order, `_with_symmetry_[F(x),G(x)*y+H(x)]`]]

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

✓ Maple. Time used: 0.063 (sec). Leaf size: 21

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

\[ y = \frac {\ln \left (2\right )+\ln \left (\frac {1}{-x^{2}+c_1}\right )}{x} \]

✓ Mathematica. Time used: 0.398 (sec). Leaf size: 23

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

\[ y(x)\to -\frac {\log \left (-\frac {x^2}{2}-c_1\right )}{x} \]

✗ Sympy

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

NotImplementedError : The given ODE -exp(x*y(x)) + Derivative(y(x), x) + y(x)/x cannot be solved by the lie group method