64.12.1 problem 1

Internal problem ID [13505]
Book : Differential Equations by Shepley L. Ross. Third edition. John Willey. New Delhi. 2004.
Section : Chapter 4, Section 4.4. Variation of parameters. Exercises page 162
Problem number : 1
Date solved : Tuesday, January 28, 2025 at 05:50:07 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: 0.036 (sec). Leaf size: 48

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

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