50.3.9 problem 1(i)

Internal problem ID [7833]
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(i)
Date solved : Wednesday, March 05, 2025 at 05:07:25 AM
CAS classification : [_linear]

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

✓ Maple. Time used: 0.002 (sec). Leaf size: 12

ode:=diff(y(x),x)+y(x)*cot(x) = 2*x*csc(x); 
dsolve(ode,y(x), singsol=all);
 

\[ y = \csc \left (x \right ) \left (x^{2}+c_{1} \right ) \]

✓ Mathematica. Time used: 0.039 (sec). Leaf size: 14

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

\[ y(x)\to \left (x^2+c_1\right ) \csc (x) \]

✓ Sympy. Time used: 0.758 (sec). Leaf size: 10

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

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