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 : Monday, January 27, 2025 at 03:24:25 PM
CAS classification : [_linear]

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

✓ Solution by Maple

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

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

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

✓ Solution by Mathematica

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

DSolve[D[y[x],x]+y[x]*Cot[x]==2*x*Csc[x],y[x],x,IncludeSingularSolutions -> True]
 

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