26.4.5 problem 2(e)

Internal problem ID [4273]
Book : Differential equations with applications and historial notes, George F. Simmons. Second edition. 1971
Section : Chapter 2, section 11, page 49
Problem number : 2(e)
Date solved : Monday, January 27, 2025 at 08:47:19 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: 0.001 (sec). Leaf size: 12

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

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

✓ Solution by Mathematica

Time used: 0.036 (sec). Leaf size: 14

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

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