85.3.4 problem 3 (c)

Internal problem ID [22440]
Book : Applied Differential Equations. By Murray R. Spiegel. 3rd edition. 1980. Pearson. ISBN 978-0130400970
Section : Chapter 1. Differential equations in general. C Exercises at page 14
Problem number : 3 (c)
Date solved : Thursday, October 02, 2025 at 08:39:27 PM
CAS classification : [_quadrature]

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

With initial conditions

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

✓ Maple. Time used: 0.015 (sec). Leaf size: 6

ode:=diff(y(x),x) = sec(y(x)); 
ic:=[y(0) = 0]; 
dsolve([ode,op(ic)],y(x), singsol=all);
 

\[ y = \arcsin \left (x \right ) \]

✓ Mathematica. Time used: 0.005 (sec). Leaf size: 7

ode=D[y[x],x]==Sec[y[x]]; 
ic={y[0]==0}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \arcsin (x) \end{align*}

✓ Sympy. Time used: 0.124 (sec). Leaf size: 5

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

\[ y{\left (x \right )} = \operatorname {asin}{\left (x \right )} \]