49.22.10 problem 2(b)

Internal problem ID [7756]
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 : 2(b)
Date solved : Monday, January 27, 2025 at 03:12:06 PM
CAS classification : [_separable]

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

✓ Solution by Maple

Time used: 0.131 (sec). Leaf size: 25

dsolve(cos(x)*cos(y(x))-2*sin(x)*sin(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: 0.442 (sec). Leaf size: 43

DSolve[Cos[x]*cos[y[x]]-(2*Sin[x]*Sin[y[x]])*D[y[x],x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to \text {InverseFunction}\left [\int _1^{\text {$\#$1}}\frac {\sin (K[1])}{\cos (K[1])}dK[1]\&\right ]\left [\frac {1}{2} \log (\sin (x))+c_1\right ] \\ y(x)\to \cos ^{(-1)}(0) \\ \end{align*}