68.4.43 problem 43

Internal problem ID [17223]
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 : 43
Date solved : Friday, October 03, 2025 at 07:30:27 AM
CAS classification : [_quadrature]

\begin{align*} 1&=\cos \left (y\right ) y^{\prime } \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=2 \\ \end{align*}

✓ Maple. Time used: 0.060 (sec). Leaf size: 13

ode:=1 = cos(y(x))*diff(y(x),x); 
ic:=[y(0) = 2]; 
dsolve([ode,op(ic)],y(x), singsol=all);
 

\[ y = -\arcsin \left (x +\sin \left (2\right )\right )+\pi \]

✗ Mathematica

ode=1==Cos[y[x]]*D[y[x],x]; 
ic={y[0]==2}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

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✓ Sympy. Time used: 0.171 (sec). Leaf size: 10

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-cos(y(x))*Derivative(y(x), x) + 1,0) 
ics = {y(0): 2} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = \pi - \operatorname {asin}{\left (x + \sin {\left (2 \right )} \right )} \]