78.6.5 problem 2 (e)

Internal problem ID [18173]
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 (e)
Date solved : Tuesday, January 28, 2025 at 11:36:10 AM
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)
 

\[ y = \left (x^{2}+c_1 \right ) \csc \left (x \right ) \]

✓ Solution by Mathematica

Time used: 0.035 (sec). Leaf size: 14

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

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