Internal problem ID [6187]
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 1.5. Exact Equations. Page
20
Problem number: 6.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
\[ \boxed {\cos \left (x \right ) \cos \left (y\right )^{2}+2 \sin \left (x \right ) \sin \left (y\right ) \cos \left (y\right ) y^{\prime }=0} \]
✓ Solution by Maple
Time used: 0.25 (sec). Leaf size: 31
dsolve((cos(x)*cos(y(x))^2)+(2*sin(x)*sin(y(x))*cos(y(x)))*diff(y(x),x)=0,y(x), singsol=all)
\begin{align*} y \left (x \right ) &= \frac {\pi }{2} \\ y \left (x \right ) &= \arccos \left (\sqrt {c_{1} \sin \left (x \right )}\right ) \\ y \left (x \right ) &= \frac {\pi }{2}+\arcsin \left (\sqrt {c_{1} \sin \left (x \right )}\right ) \\ \end{align*}
✓ Solution by Mathematica
Time used: 5.453 (sec). Leaf size: 73
DSolve[(Cos[x]*Cos[y[x]]^2)+(2*Sin[x]*Sin[y[x]]*Cos[y[x]])*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {\pi }{2} \\ y(x)\to \frac {\pi }{2} \\ y(x)\to -\arccos \left (-\frac {1}{4} c_1 \sqrt {\sin (x)}\right ) \\ y(x)\to \arccos \left (-\frac {1}{4} c_1 \sqrt {\sin (x)}\right ) \\ y(x)\to -\frac {\pi }{2} \\ y(x)\to \frac {\pi }{2} \\ \end{align*}