76.4.8 problem 8

Internal problem ID [17331]
Book : Differential equations. An introduction to modern methods and applications. James Brannan, William E. Boyce. Third edition. Wiley 2015
Section : Chapter 2. First order differential equations. Section 2.6 (Exact equations and integrating factors). Problems at page 100
Problem number : 8
Date solved : Monday, March 31, 2025 at 03:53:42 PM
CAS classification : [`x=_G(y,y')`]

\begin{align*} {\mathrm e}^{x} \sin \left (y\right )+3 y-\left (3 x -{\mathrm e}^{x} \sin \left (y\right )\right ) y^{\prime }&=0 \end{align*}

✗ Maple

ode:=exp(x)*sin(y(x))+3*y(x)-(3*x-exp(x)*sin(y(x)))*diff(y(x),x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ \text {No solution found} \]

✗ Mathematica

ode=(Exp[x]*Sin[y[x]]+3*y[x])-(3*x-Exp[x]*Sin[y[x]])*D[y[x],x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

Not solved

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq((-3*x + exp(x)*sin(y(x)))*Derivative(y(x), x) + 3*y(x) + exp(x)*sin(y(x)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

Timed Out