Internal problem ID [1892]
Book: Differential Equations, Nelson, Folley, Coral, 3rd ed, 1964
Section: Exercis 5, page 21
Problem number: 23.
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*} [y \relax (0) = 0] \end {align*}
✓ Solution by Maple
Time used: 0.256 (sec). Leaf size: 15
dsolve([sin(x)*cos(y(x))+cos(x)*sin(y(x))*diff(y(x),x)=0,y(0) = 0],y(x), singsol=all)
\[ y \relax (x ) = \arccos \left (\frac {1}{\cos \relax (x )}\right ) \left (1-2 \_B5 \right ) \]
✓ Solution by Mathematica
Time used: 2.246 (sec). Leaf size: 17
DSolve[{Sin[x]*Cos[y[x]]+Cos[x]*Sin[y[x]]*y'[x]==0,y[0]==0},y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\text {ArcCos}(\sec (x)) \\ y(x)\to \text {ArcCos}(\sec (x)) \\ \end{align*}