59.4.6 problem 9.1 (vi)

Internal problem ID [15017]
Book : AN INTRODUCTION TO ORDINARY DIFFERENTIAL EQUATIONS by JAMES C. ROBINSON. Cambridge University Press 2004
Section : Chapter 9, First order linear equations and the integrating factor. Exercises page 86
Problem number : 9.1 (vi)
Date solved : Thursday, October 02, 2025 at 10:01:11 AM
CAS classification : [_linear]

\begin{align*} y^{\prime }+2 y \cot \left (x \right )&=5 \end{align*}

With initial conditions

\begin{align*} y \left (\frac {\pi }{2}\right )&=1 \\ \end{align*}

✓ Maple. Time used: 0.029 (sec). Leaf size: 29

ode:=diff(y(x),x)+2*y(x)*cot(x) = 5; 
ic:=[y(1/2*Pi) = 1]; 
dsolve([ode,op(ic)],y(x), singsol=all);
 

\[ y = \frac {-10 x +5 \sin \left (2 x \right )-4+5 \pi }{-2+2 \cos \left (2 x \right )} \]

✓ Mathematica. Time used: 0.028 (sec). Leaf size: 27

ode=D[y[x],x]+2*y[x]*Cot[x]==5; 
ic={y[Pi/2]==1}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \frac {1}{4} (10 x-5 \sin (2 x)-5 \pi +4) \csc ^2(x) \end{align*}

✓ Sympy. Time used: 0.735 (sec). Leaf size: 27

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(2*y(x)/tan(x) + Derivative(y(x), x) - 5,0) 
ics = {y(pi/2): 1} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = \frac {\frac {5 x}{2} - \frac {5 \sin {\left (2 x \right )}}{4} - \frac {5 \pi }{4} + 1}{\sin ^{2}{\left (x \right )}} \]