8.6.23 problem 23

Internal problem ID [793]
Book : Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section : Chapter 1 review problems. Page 78
Problem number : 23
Date solved : Saturday, March 29, 2025 at 10:27:58 PM
CAS classification : [_exact]

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

✓ Maple. Time used: 0.015 (sec). Leaf size: 23

ode:=exp(y(x))+cos(x)*y(x)+(exp(y(x))*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: 3.644 (sec). Leaf size: 25

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

\[ y(x)\to c_1 \csc (x)-W\left (x \csc (x) e^{c_1 \csc (x)}\right ) \]

✗ 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