12.3.25 problem 26

Internal problem ID [1602]
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
Date solved : Monday, January 27, 2025 at 05:13:31 AM
CAS classification : [_separable]

\begin{align*} y^{\prime }&=\frac {\cos \left (x \right )}{\sin \left (y\right )} \end{align*}

With initial conditions

\begin{align*} y \left (\pi \right )&=\frac {\pi }{2} \end{align*}

✓ Solution by Maple

Time used: 0.096 (sec). Leaf size: 11

dsolve([diff(y(x),x)=cos(x)/sin(y(x)),y(Pi) = 1/2*Pi],y(x), singsol=all)
 

\[ y = \frac {\pi }{2}+\arcsin \left (\sin \left (x \right )\right ) \]

✓ Solution by Mathematica

Time used: 0.403 (sec). Leaf size: 10

DSolve[{D[y[x],x]==Cos[x]/Sin[y[x]],y[Pi]==Pi/2},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \arccos (-\sin (x)) \]