74.8.2 problem 2

Internal problem ID [16067]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 2. First Order Equations. Review exercises, page 80
Problem number : 2
Date solved : Monday, March 31, 2025 at 02:38:31 PM
CAS classification : [_separable]

\begin{align*} \cos \left (4 x \right )-8 \sin \left (y\right ) y^{\prime }&=0 \end{align*}

✓ Maple. Time used: 0.004 (sec). Leaf size: 19

ode:=cos(4*x)-8*sin(y(x))*diff(y(x),x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {\pi }{2}+\arcsin \left (\frac {\sin \left (4 x \right )}{32}+\frac {c_1}{8}\right ) \]

✓ Mathematica. Time used: 0.306 (sec). Leaf size: 37

ode=Cos[4*x]-8*Sin[y[x]]*D[y[x],x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to \text {InverseFunction}\left [\int _1^{\text {$\#$1}}\sin (K[1])dK[1]\&\right ]\left [\int _1^x\frac {1}{8} \cos (4 K[2])dK[2]+c_1\right ] \]

✓ Sympy. Time used: 0.743 (sec). Leaf size: 27

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-8*sin(y(x))*Derivative(y(x), x) + cos(4*x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ \left [ y{\left (x \right )} = - \operatorname {acos}{\left (C_{1} - \frac {\sin {\left (4 x \right )}}{32} \right )} + 2 \pi , \ y{\left (x \right )} = \operatorname {acos}{\left (C_{1} - \frac {\sin {\left (4 x \right )}}{32} \right )}\right ] \]