Internal problem ID [1892]
Book: Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath.
Boston. 1964
Section: Exercise 5, page 21
Problem number: 23.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
\[ \boxed {\cos \left (y\right ) \sin \left (x \right )+\cos \left (x \right ) \sin \left (y\right ) y^{\prime }=0} \] With initial conditions \begin {align*} [y \left (0\right ) = 0] \end {align*}
✓ Solution by Maple
Time used: 0.219 (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)
\begin{align*} y \left (x \right ) &= \frac {\pi }{2}-\arcsin \left (\sec \left (x \right )\right ) \\ y \left (x \right ) &= -\frac {\pi }{2}+\arcsin \left (\sec \left (x \right )\right ) \\ \end{align*}
✓ Solution by Mathematica
Time used: 6.227 (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 -\arccos (\sec (x)) \\ y(x)\to \arccos (\sec (x)) \\ \end{align*}