68.4.12 problem 12

Internal problem ID [17192]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 2. First Order Equations. Exercises 2.2, page 39
Problem number : 12
Date solved : Thursday, October 02, 2025 at 01:50:02 PM
CAS classification : [_separable]

\begin{align*} \cos \left (y\right ) y^{\prime }&=8 \sin \left (8 t \right ) \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 15

ode:=cos(y(t))*diff(y(t),t) = 8*sin(8*t); 
dsolve(ode,y(t), singsol=all);
 

\[ y = \arcsin \left (-\cos \left (8 t \right )+64 c_1 \right ) \]

✓ Mathematica. Time used: 0.199 (sec). Leaf size: 35

ode=Cos[y[t]]*D[y[t],t]==8*Sin[8*t]; 
ic={}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\begin{align*} y(t)&\to \text {InverseFunction}\left [\int _1^{\text {$\#$1}}\cos (K[1])dK[1]\&\right ]\left [\int _1^t8 \sin (8 K[2])dK[2]+c_1\right ] \end{align*}

✓ Sympy. Time used: 0.727 (sec). Leaf size: 22

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(-8*sin(8*t) + cos(y(t))*Derivative(y(t), t),0) 
ics = {} 
dsolve(ode,func=y(t),ics=ics)
 

\[ \left [ y{\left (t \right )} = \pi - \operatorname {asin}{\left (C_{1} - \cos {\left (8 t \right )} \right )}, \ y{\left (t \right )} = \operatorname {asin}{\left (C_{1} - \cos {\left (8 t \right )} \right )}\right ] \]