Internal problem ID [952]
Book: Elementary differential equations with boundary value problems. William F. Trench.
Brooks/Cole 2001
Section: Chapter 2, First order equations. separable equations. Section 2.2 Page 52
Problem number: 26.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
Solve \begin {gather*} \boxed {y^{\prime }-\frac {\cos \relax (x )}{\sin \relax (y)}=0} \end {gather*} With initial conditions \begin {align*} \left [y \left (\pi \right ) = \frac {\pi }{2}\right ] \end {align*}
✓ Solution by Maple
Time used: 0.5 (sec). Leaf size: 11
dsolve([diff(y(x),x)=cos(x)/sin(y(x)),y(Pi) = 1/2*Pi],y(x), singsol=all)
\[ y \relax (x ) = \frac {\pi }{2}+\arcsin \left (\sin \relax (x )\right ) \]
✓ Solution by Mathematica
Time used: 0.463 (sec). Leaf size: 10
DSolve[{y'[x]==Cos[x]/Sin[y[x]],y[Pi]==Pi/2},y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \text {ArcCos}(-\sin (x)) \\ \end{align*}