78.1.27 problem 2 (m)

Internal problem ID [18011]
Book : DIFFERENTIAL EQUATIONS WITH APPLICATIONS AND HISTORICAL NOTES by George F. Simmons. 3rd edition. 2017. CRC press, Boca Raton FL.
Section : Chapter 1. The Nature of Differential Equations. Separable Equations. Section 2. Problems at page 9
Problem number : 2 (m)
Date solved : Monday, March 31, 2025 at 04:56:33 PM
CAS classification : [_separable]

\begin{align*} y^{\prime } \sin \left (y\right )&=x^{2} \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 16

ode:=diff(y(x),x)*sin(y(x)) = x^2; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {\pi }{2}+\arcsin \left (\frac {x^{3}}{3}+c_1 \right ) \]

✓ Mathematica. Time used: 0.44 (sec). Leaf size: 37

ode=D[y[x],x]*Sin[y[x]]==x^2; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)\to -\arccos \left (-\frac {x^3}{3}-c_1\right ) \\ y(x)\to \arccos \left (-\frac {x^3}{3}-c_1\right ) \\ \end{align*}

✓ Sympy. Time used: 0.336 (sec). Leaf size: 24

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

\[ \left [ y{\left (x \right )} = - \operatorname {acos}{\left (C_{1} - \frac {x^{3}}{3} \right )} + 2 \pi , \ y{\left (x \right )} = \operatorname {acos}{\left (C_{1} - \frac {x^{3}}{3} \right )}\right ] \]