78.1.27 problem 2 (m)

Internal problem ID [18082]
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 : Tuesday, January 28, 2025 at 11:25:45 AM
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: 0.440 (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*}