74.3.29 problem 24

Internal problem ID [15818]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 2. First Order Equations. Exercises 2.1, page 32
Problem number : 24
Date solved : Monday, March 31, 2025 at 01:56:39 PM
CAS classification : [_linear]

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

With initial conditions

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

✓ Maple. Time used: 0.022 (sec). Leaf size: 11

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

\[ y = -\cos \left (t \right ) \ln \left (\cos \left (t \right )\right ) \]

✓ Mathematica. Time used: 0.049 (sec). Leaf size: 12

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

\[ y(t)\to -\cos (t) \log (\cos (t)) \]

✓ Sympy. Time used: 0.456 (sec). Leaf size: 12

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

\[ y{\left (t \right )} = - \log {\left (\cos {\left (t \right )} \right )} \cos {\left (t \right )} \]