74.3.10 problem 11

Internal problem ID [15799]
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 : Monday, March 31, 2025 at 01:49:55 PM
CAS classification : [_separable]

\begin{align*} y^{\prime }&=y \tan \left (t \right ) \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,ic],y(t), singsol=all);
 

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

✓ Mathematica. Time used: 0.03 (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]
 

\[ y(t)\to \sec (t) \]

✓ Sympy. Time used: 0.210 (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)
 

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