Internal problem ID [2048]
Book: Differential equations and linear algebra, Stephen W. Goode, second edition, 2000
Section: 1.4, page 36
Problem number: 14.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
Solve \begin {gather*} \boxed {y^{\prime }-1+\frac {\sin \left (x +y\right )}{\cos \relax (x ) \sin \relax (y)}=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: 0.359 (sec). Leaf size: 11
dsolve([diff(y(x),x)=1- (sin(x+y(x)))/(sin(y(x))*cos(x)),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: 6.078 (sec). Leaf size: 10
DSolve[{y'[x]==1- Sin[x+y[x]]/(Sin[y[x]]*Cos[x]),y[Pi/4]==Pi/4},y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \sec ^{-1}(2 \cos (x)) \\ \end{align*}