78.8.22 problem 22

Internal problem ID [18149]
Book : DIFFERENTIAL EQUATIONS WITH APPLICATIONS AND HISTORICAL NOTES by George F. Simmons. 3rd edition. 2017. CRC press, Boca Raton FL.
Section : Chapter 2. First order equations. Miscellaneous Problems for Chapter 2. Problems at page 99
Problem number : 22
Date solved : Monday, March 31, 2025 at 05:14:26 PM
CAS classification : [_exact]

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

✓ Maple. Time used: 0.011 (sec). Leaf size: 16

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

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

✓ Mathematica. Time used: 0.528 (sec). Leaf size: 19

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

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

✗ Sympy

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

Timed Out