Internal problem ID [5392]
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).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
Solve \begin {gather*} \boxed {y^{\prime } \sin \relax (y)-x^{2}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 16
dsolve(diff(y(x),x)*sin(y(x))=x^2,y(x), singsol=all)
\[ y \relax (x ) = \pi -\arccos \left (\frac {x^{3}}{3}+c_{1}\right ) \]
✓ Solution by Mathematica
Time used: 0.686 (sec). Leaf size: 37
DSolve[y'[x]*Sin[y[x]]==x^2,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\text {ArcCos}\left (-\frac {x^3}{3}-c_1\right ) \\ y(x)\to \text {ArcCos}\left (-\frac {x^3}{3}-c_1\right ) \\ \end{align*}