Internal problem ID [5335]
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).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
Solve \begin {gather*} \boxed {\cos \relax (x ) \cos \relax (y)-2 y^{\prime } \sin \relax (y) \sin \relax (x )=0} \end {gather*}
✓ Solution by Maple
Time used: 0.015 (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 \relax (x ) = \arccos \left (\frac {1}{\sqrt {\sin \relax (x ) c_{1}}}\right ) \\ y \relax (x ) = \pi -\arccos \left (\frac {1}{\sqrt {\sin \relax (x ) c_{1}}}\right ) \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.721 (sec). Leaf size: 43
DSolve[Cos[x]*cos[y[x]]-(2*Sin[x]*Sin[y[x]])*y'[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*}