16.1.10 problem 3(d)

Internal problem ID [3412]
Book : Elementary Differential Equations, Martin, Reissner, 2nd ed, 1961
Section : Exercis 2, page 5
Problem number : 3(d)
Date solved : Monday, January 27, 2025 at 07:36:01 AM
CAS classification : [_separable]

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

✓ Solution by Maple

Time used: 0.005 (sec). Leaf size: 16

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

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

✓ Solution by Mathematica

Time used: 0.450 (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*}