24.1.12 problem 3(a)

Internal problem ID [4201]
Book : Elementary Differential equations, Chaundy, 1969
Section : Exercises 3, page 60
Problem number : 3(a)
Date solved : Sunday, March 30, 2025 at 02:42:31 AM
CAS classification : [_linear]

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

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

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

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

✓ Mathematica. Time used: 0.065 (sec). Leaf size: 45

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

\[ y(x)\to x+\cos (x) \left (\log \left (\cos \left (\frac {x}{2}\right )-\sin \left (\frac {x}{2}\right )\right )-\log \left (\sin \left (\frac {x}{2}\right )+\cos \left (\frac {x}{2}\right )\right )+c_1\right ) \]

✓ Sympy. Time used: 1.513 (sec). Leaf size: 22

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

\[ - \int \frac {x \tan {\left (x \right )}}{\cos {\left (x \right )}}\, dx + \int \frac {y{\left (x \right )} \tan {\left (x \right )}}{\cos {\left (x \right )}}\, dx = C_{1} \]