78.6.7 problem 2 (g)

Internal problem ID [18175]
Book : DIFFERENTIAL EQUATIONS WITH APPLICATIONS AND HISTORICAL NOTES by George F. Simmons. 3rd edition. 2017. CRC press, Boca Raton FL.
Section : Chapter 2. First order equations. Section 10 (Linear equations). Problems at page 82
Problem number : 2 (g)
Date solved : Tuesday, January 28, 2025 at 11:36:14 AM
CAS classification : [_linear]

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

✓ Solution by Maple

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

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

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

✓ Solution by Mathematica

Time used: 0.059 (sec). Leaf size: 21

DSolve[y[x]-x+x*y[x]*Cot[x]+x*D[y[x],x]==0,y[x],x,IncludeSingularSolutions -> True]
 

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