90.3.15 problem 15

Internal problem ID [25079]
Book : Ordinary Differential Equations. By William Adkins and Mark G Davidson. Springer. NY. 2010. ISBN 978-1-4614-3617-1
Section : Chapter 1. First order differential equations. Exercises at page 41
Problem number : 15
Date solved : Thursday, October 02, 2025 at 11:49:30 PM
CAS classification : [_separable]

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

✓ Maple. Time used: 0.000 (sec). Leaf size: 10

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

\[ y = \cos \left (t \right ) c_1 +1 \]

✓ Mathematica. Time used: 0.035 (sec). Leaf size: 17

ode=D[y[t],{t,1}] + Tan[t]*y[t]==Tan[t]; 
ic={}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\begin{align*} y(t)&\to 1+c_1 \cos (t)\\ y(t)&\to 1 \end{align*}

✓ Sympy. Time used: 0.143 (sec). Leaf size: 8

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

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