49.22.4 problem 1(d)

Internal problem ID [7750]
Book : An introduction to Ordinary Differential Equations. Earl A. Coddington. Dover. NY 1961
Section : Chapter 5. Existence and uniqueness of solutions to first order equations. Page 198
Problem number : 1(d)
Date solved : Monday, January 27, 2025 at 03:12:01 PM
CAS classification : [_separable]

\begin{align*} \cos \left (x \right ) \cos \left (y\right )^{2}-\sin \left (x \right ) \sin \left (2 y\right ) y^{\prime }&=0 \end{align*}

✓ Solution by Maple

Time used: 0.133 (sec). Leaf size: 25

dsolve(cos(x)*cos(y(x))^2-sin(x)*sin(2*y(x))*diff(y(x),x)=0,y(x), singsol=all)
 

\begin{align*} y &= \arccos \left (\frac {1}{\sqrt {\sin \left (x \right ) c_{1}}}\right ) \\ y &= \frac {\pi }{2}+\arcsin \left (\frac {1}{\sqrt {\sin \left (x \right ) c_{1}}}\right ) \\ \end{align*}

✓ Solution by Mathematica

Time used: 5.845 (sec). Leaf size: 73

DSolve[Cos[x]*Cos[y[x]]^2-Sin[x]*Sin[2*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 {c_1}{4 \sqrt {\sin (x)}}\right ) \\ y(x)\to \arccos \left (-\frac {c_1}{4 \sqrt {\sin (x)}}\right ) \\ y(x)\to -\frac {\pi }{2} \\ y(x)\to \frac {\pi }{2} \\ \end{align*}