10.3.3 problem 3

Internal problem ID [1168]
Book : Elementary differential equations and boundary value problems, 10th ed., Boyce and DiPrima
Section : Section 2.4. Page 76
Problem number : 3
Date solved : Saturday, March 29, 2025 at 10:44:14 PM
CAS classification : [_linear]

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

With initial conditions

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

✓ Maple. Time used: 0.029 (sec). Leaf size: 16

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

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

✓ Mathematica. Time used: 0.054 (sec). Leaf size: 20

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

\[ y(t)\to i \cos (t) (\pi +i \log (\cos (t))) \]

✓ Sympy. Time used: 0.468 (sec). Leaf size: 14

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

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