50.2.7 problem 1(g)

Internal problem ID [7813]
Book : Differential Equations: Theory, Technique, and Practice by George Simmons, Steven Krantz. McGraw-Hill NY. 2007. 1st Edition.
Section : Chapter 1. What is a differential equation. Section 1.3 SEPARABLE EQUATIONS. Page 12
Problem number : 1(g)
Date solved : Wednesday, March 05, 2025 at 05:06:48 AM
CAS classification : [_separable]

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

✓ Maple. Time used: 0.004 (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: 0.499 (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: 0.350 (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)
 

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