68.6.4 problem 4

Internal problem ID [17314]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 2. First Order Equations. Exercises 2.4, page 57
Problem number : 4
Date solved : Thursday, October 02, 2025 at 02:02:07 PM
CAS classification : [_linear]

\begin{align*} \sec \left (t \right )^{2} y+2 t +\tan \left (t \right ) y^{\prime }&=0 \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 14

ode:=y(t)*sec(t)^2+2*t+tan(t)*diff(y(t),t) = 0; 
dsolve(ode,y(t), singsol=all);
 

\[ y = \left (-t^{2}+c_1 \right ) \cot \left (t \right ) \]

✓ Mathematica. Time used: 0.036 (sec). Leaf size: 16

ode=(y[t]*Sec[t]^2+2*t)+Tan[t]*D[y[t],t]==0; 
ic={}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\begin{align*} y(t)&\to \left (-t^2+c_1\right ) \cot (t) \end{align*}

✗ Sympy

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(2*t + y(t)/cos(t)**2 + tan(t)*Derivative(y(t), t),0) 
ics = {} 
dsolve(ode,func=y(t),ics=ics)
 

Timed Out