78.8.40 problem 40

Internal problem ID [18167]
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 : 40
Date solved : Monday, March 31, 2025 at 05:20:49 PM
CAS classification : [_exact]

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

✓ Maple. Time used: 0.009 (sec). Leaf size: 20

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

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

✓ Mathematica. Time used: 0.274 (sec). Leaf size: 23

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

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

✗ Sympy

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

Timed Out