26.5.18 problem 22

Internal problem ID [4292]
Book : Differential equations with applications and historial notes, George F. Simmons. Second edition. 1971
Section : Chapter 2, End of chapter, page 61
Problem number : 22
Date solved : Sunday, March 30, 2025 at 02:51:51 AM
CAS classification : [_exact]

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

✓ Maple. Time used: 0.012 (sec). Leaf size: 16

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

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

✓ Mathematica. Time used: 0.558 (sec). Leaf size: 19

ode=(Exp[x]*Sin[y[x]]-y[x]*Sin[x*y[x]])+(Exp[x]*Cos[y[x]]-x*Sin[x*y[x]])*D[y[x],x]==0; 
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)) + exp(x)*cos(y(x)))*Derivative(y(x), x) - y(x)*sin(x*y(x)) + exp(x)*sin(y(x)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

Timed Out