Internal problem ID [3958]
Book: Ordinary Differential Equations, By Tenenbaum and Pollard. Dover, NY 1963
Section: Chapter 2. Special types of differential equations of the first kind. Lesson 9
Problem number: Exact Differential equations. Exercise 9.16, page 79.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
Solve \begin {gather*} \boxed {\cos \relax (y) \sin \relax (x )+\cos \relax (x ) \sin \relax (y) y^{\prime }=0} \end {gather*} With initial conditions \begin {align*} \left [y \left (\frac {\pi }{4}\right ) = \frac {\pi }{4}\right ] \end {align*}
✓ Solution by Maple
Time used: 0.625 (sec). Leaf size: 11
dsolve([sin(x)*cos(y(x))+cos(x)*sin(y(x))*diff(y(x),x)=0,y(1/4*Pi) = 1/4*Pi],y(x), singsol=all)
\[ y \relax (x ) = \arccos \left (\frac {1}{2 \cos \relax (x )}\right ) \]
✓ Solution by Mathematica
Time used: 5.979 (sec). Leaf size: 10
DSolve[{Sin[x]*Cos[y[x]]+Cos[x]*Sin[y[x]]*y'[x]==0,y[Pi/4]==Pi/4},y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \sec ^{-1}(2 \cos (x)) \\ \end{align*}