1.7.23 problem 23

Internal problem ID [201]
Book : Elementary Differential Equations. By C. Henry Edwards, David E. Penney and David Calvis. 6th edition. 2008
Section : Chapter 1. First order differential equations. Review problems at page 98
Problem number : 23
Date solved : Tuesday, September 30, 2025 at 03:51:45 AM
CAS classification : [_exact]

\begin{align*} {\mathrm e}^{y}+y \cos \left (x \right )+\left (x \,{\mathrm e}^{y}+\sin \left (x \right )\right ) y^{\prime }&=0 \end{align*}

✓ Maple. Time used: 0.014 (sec). Leaf size: 23

ode:=exp(y(x))+y(x)*cos(x)+(x*exp(y(x))+sin(x))*diff(y(x),x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = -\operatorname {LambertW}\left (x \,{\mathrm e}^{-c_1 \csc \left (x \right )} \csc \left (x \right )\right )-c_1 \csc \left (x \right ) \]

✓ Mathematica. Time used: 3.507 (sec). Leaf size: 25

ode=Exp[y[x]]+y[x]*Cos[x]+(x*Exp[y[x]]+Sin[x])*D[y[x],x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to c_1 \csc (x)-W\left (x \csc (x) e^{c_1 \csc (x)}\right ) \end{align*}

✗ Sympy

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

Timed Out