44.8.4 problem 1(d)

Internal problem ID [9206]
Book : Differential Equations: Theory, Technique, and Practice by George Simmons, Steven Krantz. McGraw-Hill NY. 2007. 1st Edition.
Section : Chapter 1. What is a differential equation. Problems for Review and Discovery. Page 53
Problem number : 1(d)
Date solved : Tuesday, September 30, 2025 at 06:14:33 PM
CAS classification : [_separable]

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

✓ Maple. Time used: 0.003 (sec). Leaf size: 9

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

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

✓ Mathematica. Time used: 0.122 (sec). Leaf size: 31

ode=Sec[x]*D[y[x],x]==Sec[y[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\cos (K[2])dK[2]+c_1\right ] \end{align*}

✓ Sympy. Time used: 0.255 (sec). Leaf size: 19

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

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