59.1.6 problem 5.4 (i)

Internal problem ID [14990]
Book : AN INTRODUCTION TO ORDINARY DIFFERENTIAL EQUATIONS by JAMES C. ROBINSON. Cambridge University Press 2004
Section : Chapter 5, Trivial differential equations. Exercises page 33
Problem number : 5.4 (i)
Date solved : Thursday, October 02, 2025 at 09:58:07 AM
CAS classification : [_quadrature]

\begin{align*} x^{\prime }&=\sec \left (t \right )^{2} \end{align*}

With initial conditions

\begin{align*} x \left (\frac {\pi }{4}\right )&=0 \\ \end{align*}

✓ Maple. Time used: 0.018 (sec). Leaf size: 8

ode:=diff(x(t),t) = sec(t)^2; 
ic:=[x(1/4*Pi) = 0]; 
dsolve([ode,op(ic)],x(t), singsol=all);
 

\[ x = \tan \left (t \right )-1 \]

✓ Mathematica. Time used: 0.005 (sec). Leaf size: 9

ode=D[x[t],t]==Sec[t]^2; 
ic={x[Pi/4]==0}; 
DSolve[{ode,ic},x[t],t,IncludeSingularSolutions->True]
 

\begin{align*} x(t)&\to \tan (t)-1 \end{align*}

✓ Sympy. Time used: 0.087 (sec). Leaf size: 10

from sympy import * 
t = symbols("t") 
x = Function("x") 
ode = Eq(Derivative(x(t), t) - 1/cos(t)**2,0) 
ics = {x(pi/4): 0} 
dsolve(ode,func=x(t),ics=ics)
 

\[ x{\left (t \right )} = \frac {\sin {\left (t \right )}}{\cos {\left (t \right )}} - 1 \]