81.2.4 problem 3-4

Internal problem ID [21493]
Book : The Differential Equations Problem Solver. VOL. I. M. Fogiel director. REA, NY. 1978. ISBN 78-63609
Section : Chapter 3. Exact differential equations. Page 42.
Problem number : 3-4
Date solved : Thursday, October 02, 2025 at 07:41:58 PM
CAS classification : [NONE]

\begin{align*} y^{\prime }+\frac {2 x \sin \left (y\right )+y^{3} {\mathrm e}^{x}}{x^{2} \cos \left (y\right )+3 y^{2} {\mathrm e}^{x}}&=0 \end{align*}

✓ Maple. Time used: 0.023 (sec). Leaf size: 19

ode:=diff(y(x),x)+(2*x*sin(y(x))+y(x)^3*exp(x))/(x^2*cos(y(x))+3*y(x)^2*exp(x)) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y^{3} {\mathrm e}^{x}+\sin \left (y\right ) x^{2}+c_1 = 0 \]

✓ Mathematica. Time used: 0.259 (sec). Leaf size: 22

ode=D[y[x],x] +  ( 2*x*Sin[y[x]]+y[x]^3*Exp[x]  )/( x^2*Cos[y[x]]+3*y[x]^2*Exp[x]   )  ==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ \text {Solve}\left [x^2 \sin (y(x))+e^x y(x)^3=c_1,y(x)\right ] \]

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq((2*x*sin(y(x)) + y(x)**3*exp(x))/(x**2*cos(y(x)) + 3*y(x)**2*exp(x)) + Derivative(y(x), x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

Timed Out