90.3.28 problem 28

Internal problem ID [25092]
Book : Ordinary Differential Equations. By William Adkins and Mark G Davidson. Springer. NY. 2010. ISBN 978-1-4614-3617-1
Section : Chapter 1. First order differential equations. Exercises at page 41
Problem number : 28
Date solved : Thursday, October 02, 2025 at 11:49:56 PM
CAS classification : [_separable]

\begin{align*} y^{\prime }&=\frac {\cot \left (y\right )}{t} \end{align*}

With initial conditions

\begin{align*} y \left (1\right )&=\frac {\pi }{4} \\ \end{align*}

✓ Maple. Time used: 0.063 (sec). Leaf size: 13

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

\[ y = \arccos \left (\frac {\sqrt {2}}{2 t}\right ) \]

✓ Mathematica. Time used: 22.787 (sec). Leaf size: 15

ode=D[y[t],{t,1}] ==Cot[y[t]]/t; 
ic={y[1]==Pi/4}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\begin{align*} y(t)&\to \arccos \left (\frac {1}{\sqrt {2} t}\right ) \end{align*}

✓ Sympy. Time used: 0.191 (sec). Leaf size: 12

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(Derivative(y(t), t) - cot(y(t))/t,0) 
ics = {y(1): pi/4} 
dsolve(ode,func=y(t),ics=ics)
 

\[ y{\left (t \right )} = \operatorname {acos}{\left (\frac {\sqrt {2}}{2 t} \right )} \]