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 : Sunday, March 30, 2025 at 12:03:22 AM
CAS classification : [_separable]

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

✓ Maple. Time used: 0.037 (sec). Leaf size: 9

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

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

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

ode=Cos[y[t]]*Sin[t]*D[y[t],t]==Sin[y[t]]*Cos[t]; 
ic={}; 
DSolve[{ode,ic},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*}

✓ Sympy. Time used: 0.475 (sec). Leaf size: 19

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(sin(t)*cos(y(t))*Derivative(y(t), t) - sin(y(t))*cos(t),0) 
ics = {} 
dsolve(ode,func=y(t),ics=ics)
 

\[ \left [ y{\left (t \right )} = \pi - \operatorname {asin}{\left (C_{1} \sin {\left (t \right )} \right )}, \ y{\left (t \right )} = \operatorname {asin}{\left (C_{1} \sin {\left (t \right )} \right )}\right ] \]