72.4.11 problem 12

Internal problem ID [19420]
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. Section 8 (Exact Equations). Problems at page 72
Problem number : 12
Date solved : Thursday, October 02, 2025 at 04:25:21 PM
CAS classification : [_exact]

\begin{align*} 2 x y^{4}+\sin \left (y\right )+\left (4 x^{2} y^{3}+x \cos \left (y\right )\right ) y^{\prime }&=0 \end{align*}

✓ Maple. Time used: 0.014 (sec). Leaf size: 18

ode:=2*x*y(x)^4+sin(y(x))+(4*x^2*y(x)^3+x*cos(y(x)))*diff(y(x),x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ x^{2} y^{4}+x \sin \left (y\right )+c_1 = 0 \]

✓ Mathematica. Time used: 0.192 (sec). Leaf size: 20

ode=(2*x*y[x]^4+Sin[y[x]])+ (4*x^2*y[x]^3+x*Cos[y[x]])*D[y[x],x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ \text {Solve}\left [x^2 y(x)^4+x \sin (y(x))=c_1,y(x)\right ] \]

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(2*x*y(x)**4 + (4*x**2*y(x)**3 + x*cos(y(x)))*Derivative(y(x), x) + sin(y(x)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

Timed Out