24.1.13 problem 3(b)

Internal problem ID [4202]
Book : Elementary Differential equations, Chaundy, 1969
Section : Exercises 3, page 60
Problem number : 3(b)
Date solved : Sunday, March 30, 2025 at 02:42:34 AM
CAS classification : [_linear]

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

✓ Maple. Time used: 0.002 (sec). Leaf size: 23

ode:=cot(x)*diff(y(x),x)+y(x) = tan(x); 
dsolve(ode,y(x), singsol=all);
 

\[ y = -\frac {\cos \left (x \right ) \ln \left (\sec \left (x \right )+\tan \left (x \right )\right )}{2}+\cos \left (x \right ) c_1 +\frac {\tan \left (x \right )}{2} \]

✓ Mathematica. Time used: 0.058 (sec). Leaf size: 25

ode=Cot[x]*D[y[x],x]+y[x]==Tan[x]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to \frac {1}{2} (\cos (x) (-\text {arctanh}(\sin (x)))+\tan (x)+2 c_1 \cos (x)) \]

✓ Sympy. Time used: 0.736 (sec). Leaf size: 36

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

\[ y{\left (x \right )} = C_{1} \cos {\left (x \right )} + \frac {\log {\left (\sin {\left (x \right )} - 1 \right )} \cos {\left (x \right )}}{4} - \frac {\log {\left (\sin {\left (x \right )} + 1 \right )} \cos {\left (x \right )}}{4} + \frac {\tan {\left (x \right )}}{2} \]