11.8.1 problem 1.2-3 (a)

Internal problem ID [3453]
Book : Ordinary Differential Equations, Robert H. Martin, 1983
Section : Problem 1.2-3, page 12
Problem number : 1.2-3 (a)
Date solved : Tuesday, September 30, 2025 at 06:38:47 AM
CAS classification : [_separable]

\begin{align*} y^{\prime }+4 \tan \left (2 t \right ) y&=\tan \left (2 t \right ) \end{align*}

With initial conditions

\begin{align*} y \left (\frac {\pi }{8}\right )&=2 \\ \end{align*}

✓ Maple. Time used: 0.032 (sec). Leaf size: 12

ode:=diff(y(t),t)+4*tan(2*t)*y(t) = tan(2*t); 
ic:=[y(1/8*Pi) = 2]; 
dsolve([ode,op(ic)],y(t), singsol=all);
 

\[ y = 2+\frac {7 \cos \left (4 t \right )}{4} \]

✓ Mathematica. Time used: 0.055 (sec). Leaf size: 15

ode=D[y[t],t]+4*Tan[2*t]*y[t]==Tan[2*t]; 
ic=y[Pi/8]==2; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\begin{align*} y(t)&\to \frac {7}{4} \cos (4 t)+2 \end{align*}

✓ Sympy. Time used: 0.254 (sec). Leaf size: 15

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(4*y(t)*tan(2*t) - tan(2*t) + Derivative(y(t), t),0) 
ics = {y(pi/8): 2} 
dsolve(ode,func=y(t),ics=ics)
 

\[ y{\left (t \right )} = \frac {7 \cos ^{2}{\left (2 t \right )}}{2} + \frac {1}{4} \]