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 : Monday, January 27, 2025 at 03:23:52 PM
CAS classification : [_separable]

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

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 16

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

\[ y = \frac {\pi }{2}+\arcsin \left (\frac {x^{3}}{3}+c_{1} \right ) \]

✓ Solution by Mathematica

Time used: 0.499 (sec). Leaf size: 37

DSolve[D[y[x],x]*Sin[y[x]]==x^2,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*}