17.7.4 problem 1.2-2 (d)

Internal problem ID [3450]
Book : Ordinary Differential Equations, Robert H. Martin, 1983
Section : Problem 1.2-2, page 12
Problem number : 1.2-2 (d)
Date solved : Tuesday, March 04, 2025 at 04:39:36 PM
CAS classification : [_linear]

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

With initial conditions

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

✓ Maple. Time used: 0.004 (sec). Leaf size: 6

ode:=diff(y(t),t) = -y(t)*tan(t)+sec(t); 
ic:=y(0) = 0; 
dsolve([ode,ic],y(t), singsol=all);
 

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

✓ Mathematica. Time used: 0.037 (sec). Leaf size: 7

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

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

✓ Sympy. Time used: 0.681 (sec). Leaf size: 5

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

\[ y{\left (t \right )} = \sin {\left (t \right )} \]