11.8.4 problem 1.2-3 (d)

Internal problem ID [3456]
Book : Ordinary Differential Equations, Robert H. Martin, 1983
Section : Problem 1.2-3, page 12
Problem number : 1.2-3 (d)
Date solved : Tuesday, September 30, 2025 at 06:38:53 AM
CAS classification : [_linear]

\begin{align*} y^{\prime }&=-\cot \left (t \right ) y+6 \cos \left (t \right )^{2} \end{align*}

With initial conditions

\begin{align*} y \left (\frac {\pi }{4}\right )&=3 \\ \end{align*}

✓ Maple. Time used: 0.055 (sec). Leaf size: 18

ode:=diff(y(t),t) = -cot(t)*y(t)+6*cos(t)^2; 
ic:=[y(1/4*Pi) = 3]; 
dsolve([ode,op(ic)],y(t), singsol=all);
 

\[ y = 2 \left (-\cos \left (t \right )^{3}+\sqrt {2}\right ) \csc \left (t \right ) \]

✓ Mathematica. Time used: 0.033 (sec). Leaf size: 23

ode=D[y[t],t]==-Cot[t]*y[t]+6*Cos[t]^2; 
ic=y[Pi/4]==3; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\begin{align*} y(t)&\to 2 \sqrt {2} \csc (t)-2 \cos ^2(t) \cot (t) \end{align*}

✓ Sympy. Time used: 0.878 (sec). Leaf size: 19

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(y(t)/tan(t) - 6*cos(t)**2 + Derivative(y(t), t),0) 
ics = {y(pi/4): 3} 
dsolve(ode,func=y(t),ics=ics)
 

\[ y{\left (t \right )} = \frac {- 2 \cos ^{3}{\left (t \right )} + 2 \sqrt {2}}{\sin {\left (t \right )}} \]