11.6.7 problem 1.2-1 (g)

Internal problem ID [3444]
Book : Ordinary Differential Equations, Robert H. Martin, 1983
Section : Problem 1.2-1, page 12
Problem number : 1.2-1 (g)
Date solved : Tuesday, September 30, 2025 at 06:38:32 AM
CAS classification : [_linear]

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

✓ Maple. Time used: 0.001 (sec). Leaf size: 10

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

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

✓ Mathematica. Time used: 0.02 (sec). Leaf size: 12

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

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

✓ Sympy. Time used: 0.433 (sec). Leaf size: 8

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

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