24.1.4 problem 1(d)

Internal problem ID [4193]
Book : Elementary Differential equations, Chaundy, 1969
Section : Exercises 3, page 60
Problem number : 1(d)
Date solved : Tuesday, March 04, 2025 at 05:55:22 PM
CAS classification : [_linear]

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

✓ Maple. Time used: 0.001 (sec). Leaf size: 19

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

\[ y \left (x \right ) = \csc \left (x \right ) \left (-\sin \left (x \right )+\ln \left (\sec \left (x \right )+\tan \left (x \right )\right )+c_{1} \right ) \]

✓ Mathematica. Time used: 0.04 (sec). Leaf size: 18

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

\[ y(x)\to \csc (x) \text {arctanh}(\sin (x))+c_1 \csc (x)-1 \]

✓ Sympy. Time used: 0.828 (sec). Leaf size: 32

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

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