26.2.6 problem 6

Internal problem ID [4255]
Book : Differential equations with applications and historial notes, George F. Simmons. Second edition. 1971
Section : Chapter 2, section 8, page 41
Problem number : 6
Date solved : Monday, January 27, 2025 at 08:45:22 AM
CAS classification : [_separable]

\begin{align*} \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 \end{align*}

✓ Solution by Maple

Time used: 0.327 (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: 5.126 (sec). Leaf size: 73

DSolve[Cos[x]*Cos[y[x]]^2+(2*Sin[x]*Sin[y[x]]*Cos[y[x]])*D[y[x],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*}