32.4.13 problem Recognizable Exact Differential equations. Integrating factors. Exercise 10.5, page 90

Internal problem ID [5824]
Book : Ordinary Differential Equations, By Tenenbaum and Pollard. Dover, NY 1963
Section : Chapter 2. Special types of differential equations of the first kind. Lesson 10
Problem number : Recognizable Exact Differential equations. Integrating factors. Exercise 10.5, page 90
Date solved : Sunday, March 30, 2025 at 10:18:51 AM
CAS classification : [_exact]

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

✓ Maple. Time used: 0.087 (sec). Leaf size: 18

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

\[ {\mathrm e}^{x} \sin \left (y\right )+x \,{\mathrm e}^{-y}+c_1 = 0 \]

✓ Mathematica. Time used: 0.368 (sec). Leaf size: 24

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

\[ \text {Solve}\left [x \left (-e^{-y(x)}\right )-e^x \sin (y(x))=c_1,y(x)\right ] \]

✗ Sympy

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

Timed Out