11.6.9 problem 1.2-1 (i)

Internal problem ID [3446]
Book : Ordinary Differential Equations, Robert H. Martin, 1983
Section : Problem 1.2-1, page 12
Problem number : 1.2-1 (i)
Date solved : Tuesday, September 30, 2025 at 06:38:36 AM
CAS classification : [_linear]

\begin{align*} y^{\prime }&=y \tan \left (t \right )+\sec \left (t \right )^{3} \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 11

ode:=diff(y(t),t) = y(t)*tan(t)+sec(t)^3; 
dsolve(ode,y(t), singsol=all);
 

\[ y = \left (\tan \left (t \right )+c_1 \right ) \sec \left (t \right ) \]

✓ Mathematica. Time used: 0.029 (sec). Leaf size: 13

ode=D[y[t],t]==y[t]*Tan[t]+Sec[t]^3; 
ic={}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\begin{align*} y(t)&\to \sec (t) (\tan (t)+c_1) \end{align*}

✓ Sympy. Time used: 1.430 (sec). Leaf size: 10

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(-y(t)*tan(t) + Derivative(y(t), t) - 1/cos(t)**3,0) 
ics = {} 
dsolve(ode,func=y(t),ics=ics)
 

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