68.5.13 problem 13

Internal problem ID [17264]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 2. First Order Equations. Exercises 2.3, page 49
Problem number : 13
Date solved : Thursday, October 02, 2025 at 02:00:16 PM
CAS classification : [_linear]

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

✓ Maple. Time used: 0.001 (sec). Leaf size: 19

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

\[ y = -\frac {\left (2 \cos \left (t \right )^{2}-4 c_1 -1\right ) \csc \left (t \right )}{4} \]

✓ Mathematica. Time used: 0.025 (sec). Leaf size: 19

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

\begin{align*} y(t)&\to -\frac {1}{2} \cos (t) \cot (t)+c_1 \csc (t) \end{align*}

✓ Sympy. Time used: 0.692 (sec). Leaf size: 14

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

\[ y{\left (t \right )} = \frac {C_{1} - \frac {\cos ^{2}{\left (t \right )}}{2}}{\sin {\left (t \right )}} \]