65.1.6 problem 5.4 (i)

Internal problem ID [13709]
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 : Tuesday, January 28, 2025 at 05:55:44 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*}

✓ Solution by Maple

Time used: 0.057 (sec). Leaf size: 8

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

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

✓ Solution by Mathematica

Time used: 0.006 (sec). Leaf size: 9

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

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