Internal problem ID [5334]
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]
\[ \boxed {-2 y^{\prime } \sin \left (y\right ) \sin \left (x \right )+\cos \left (x \right ) \cos \left (y\right )=0} \]
✓ Solution by Maple
Time used: 0.0 (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 \left (x \right ) = \arccos \left (\frac {1}{\sqrt {c_{1} \sin \left (x \right )}}\right ) \\ y \left (x \right ) = \pi -\arccos \left (\frac {1}{\sqrt {c_{1} \sin \left (x \right )}}\right ) \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.505 (sec). Leaf size: 47
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 (\tan (x))+\log (\cos (x)))+c_1\right ] \\ y(x)\to \cos ^{(-1)}(0) \\ \end{align*}