44.3.10 problem 1(j)

Internal problem ID [9120]
Book : Differential Equations: Theory, Technique, and Practice by George Simmons, Steven Krantz. McGraw-Hill NY. 2007. 1st Edition.
Section : Chapter 1. What is a differential equation. Section 1.4 First Order Linear Equations. Page 15
Problem number : 1(j)
Date solved : Tuesday, September 30, 2025 at 06:04:42 PM
CAS classification : [_linear]

\begin{align*} y-x +x y \cot \left (x \right )+x y^{\prime }&=0 \end{align*}

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

ode:=y(x)-x+x*y(x)*cot(x)+x*diff(y(x),x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {1-\cot \left (x \right ) x +c_1 \csc \left (x \right )}{x} \]

✓ Mathematica. Time used: 0.044 (sec). Leaf size: 27

ode=y[x]-x+x*y[x]*Cot[x]+x*D[y[x],x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \frac {\csc (x) \left (\int _1^xK[1] \sin (K[1])dK[1]+c_1\right )}{x} \end{align*}

✓ Sympy. Time used: 0.399 (sec). Leaf size: 27

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

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