65.1.6 problem 5.4 (i)

Internal problem ID [13630]
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 : Wednesday, March 05, 2025 at 10:05:36 PM
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: 0.057 (sec). Leaf size: 8

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

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

✓ Mathematica. Time used: 0.006 (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]
 

\[ x(t)\to \tan (t)-1 \]

✓ Sympy. Time used: 0.139 (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)
 

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