67.3.15 problem 4.4 (e)

Internal problem ID [16336]
Book : Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell. second edition. CRC Press. FL, USA. 2020
Section : Chapter 4. SEPARABLE FIRST ORDER EQUATIONS. Additional exercises. page 90
Problem number : 4.4 (e)
Date solved : Thursday, October 02, 2025 at 01:20:58 PM
CAS classification : [_separable]

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

✓ Maple. Time used: 0.003 (sec). Leaf size: 11

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

\[ y = \arcsin \left (-\cos \left (x \right )+c_1 \right ) \]

✓ Mathematica. Time used: 0.126 (sec). Leaf size: 31

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

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

✓ Sympy. Time used: 0.293 (sec). Leaf size: 19

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

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