73.16.2 problem 24.1 (b)

Internal problem ID [15514]
Book : Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell. second edition. CRC Press. FL, USA. 2020
Section : Chapter 24. Variation of parameters. Additional exercises page 444
Problem number : 24.1 (b)
Date solved : Tuesday, January 28, 2025 at 08:00:42 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

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

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 24

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

\[ y = \sin \left (x \right ) c_{2} +\cos \left (x \right ) c_{1} +\sin \left (x \right ) \ln \left (\csc \left (x \right )-\cot \left (x \right )\right ) \]

✓ Solution by Mathematica

Time used: 0.037 (sec). Leaf size: 48

DSolve[D[y[x],{x,2}]+y[x]==Cot[x],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \cos (x) \int _1^x-\cos (K[1])dK[1]+\sin (x) \int _1^x\cos (K[2]) \cot (K[2])dK[2]+c_1 \cos (x)+c_2 \sin (x) \]