72.1.21 problem 24

Internal problem ID [14542]
Book : DIFFERENTIAL EQUATIONS by Paul Blanchard, Robert L. Devaney, Glen R. Hall. 4th edition. Brooks/Cole. Boston, USA. 2012
Section : Chapter 1. First-Order Differential Equations. Exercises section 1.2. page 33
Problem number : 24
Date solved : Thursday, March 13, 2025 at 03:33:08 AM
CAS classification : [_quadrature]

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

✓ Maple. Time used: 0.005 (sec). Leaf size: 8

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

\[ y = \arcsin \left (x +c_{1} \right ) \]

✓ Mathematica. Time used: 0.197 (sec). Leaf size: 22

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

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

✓ Sympy. Time used: 0.209 (sec). Leaf size: 15

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

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