65.5.4 problem 10.1 (iv)

Internal problem ID [13672]
Book : AN INTRODUCTION TO ORDINARY DIFFERENTIAL EQUATIONS by JAMES C. ROBINSON. Cambridge University Press 2004
Section : Chapter 10, Two tricks for nonlinear equations. Exercises page 97
Problem number : 10.1 (iv)
Date solved : Monday, March 31, 2025 at 08:07:53 AM
CAS classification : [_exact]

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

✓ Maple. Time used: 0.008 (sec). Leaf size: 18

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

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

✓ Mathematica. Time used: 0.389 (sec). Leaf size: 22

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

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

✗ Sympy

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

Timed Out