15.8.24 problem 25

Internal problem ID [3027]
Book : Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath. Boston. 1964
Section : Exercise 12, page 46
Problem number : 25
Date solved : Monday, January 27, 2025 at 07:09:25 AM
CAS classification : [_linear]

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

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 14

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

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

✓ Solution by Mathematica

Time used: 0.041 (sec). Leaf size: 16

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

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