68.3.10 problem 11

Internal problem ID [17157]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 2. First Order Equations. Exercises 2.1, page 32
Problem number : 11
Date solved : Thursday, October 02, 2025 at 01:45:26 PM
CAS classification : [_separable]

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

With initial conditions

\begin{align*} y \left (0\right )&=1 \\ \end{align*}

✓ Maple. Time used: 0.017 (sec). Leaf size: 6

ode:=diff(y(t),t) = y(t)*tan(t); 
ic:=[y(0) = 1]; 
dsolve([ode,op(ic)],y(t), singsol=all);
 

\[ y = \sec \left (t \right ) \]

✓ Mathematica. Time used: 0.02 (sec). Leaf size: 7

ode=D[y[t],t]==y[t]*Tan[t]; 
ic={y[0]==1}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\begin{align*} y(t)&\to \sec (t) \end{align*}

✓ Sympy. Time used: 0.130 (sec). Leaf size: 7

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(-y(t)*tan(t) + Derivative(y(t), t),0) 
ics = {y(0): 1} 
dsolve(ode,func=y(t),ics=ics)
 

\[ y{\left (t \right )} = \frac {1}{\cos {\left (t \right )}} \]