14.2.5 problem 5

Internal problem ID [2493]
Book : Differential equations and their applications, 4th ed., M. Braun
Section : Chapter 1. First order differential equations. Section 1.4 separable equations. Excercises page 24
Problem number : 5
Date solved : Monday, January 27, 2025 at 05:54:20 AM
CAS classification : [_separable]

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

✓ Solution by Maple

Time used: 0.061 (sec). Leaf size: 9

dsolve(cos(y(t))*sin(t)*diff(y(t),t)=sin(y(t))*cos(t),y(t), singsol=all)
 

\[ y = \arcsin \left (c_1 \sin \left (t \right )\right ) \]

✓ Solution by Mathematica

Time used: 2.905 (sec). Leaf size: 19

DSolve[Cos[y[t]]*Sin[t]*D[y[t],t]==Sin[y[t]]*Cos[t],y[t],t,IncludeSingularSolutions -> True]
 

\begin{align*} y(t)\to \arcsin \left (\frac {1}{2} c_1 \sin (t)\right ) \\ y(t)\to 0 \\ \end{align*}