13.2.19 problem 23

Internal problem ID [2317]
Book : Differential equations and their applications, 3rd ed., M. Braun
Section : Section 1.2. Page 9
Problem number : 23
Date solved : Saturday, March 29, 2025 at 11:53:55 PM
CAS classification : [_linear]

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

✓ Maple. Time used: 0.001 (sec). Leaf size: 13

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

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

✓ Mathematica. Time used: 0.038 (sec). Leaf size: 15

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

\[ y(t)\to \cos (t) (-\cos (t)+c_1) \]

✓ Sympy. Time used: 0.776 (sec). Leaf size: 10

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

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