24.1.3 problem 1(c)

Internal problem ID [4192]
Book : Elementary Differential equations, Chaundy, 1969
Section : Exercises 3, page 60
Problem number : 1(c)
Date solved : Monday, January 27, 2025 at 08:41:41 AM
CAS classification : [_linear]

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

✓ Solution by Maple

Time used: 0.001 (sec). Leaf size: 15

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

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

✓ Solution by Mathematica

Time used: 0.040 (sec). Leaf size: 17

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

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