32.9.2 problem Exercise 22.2, page 240

Internal problem ID [5976]
Book : Ordinary Differential Equations, By Tenenbaum and Pollard. Dover, NY 1963
Section : Chapter 4. Higher order linear differential equations. Lesson 22. Variation of Parameters
Problem number : Exercise 22.2, page 240
Date solved : Monday, January 27, 2025 at 01:29:46 PM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

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

✓ Solution by Maple

Time used: 0.001 (sec). Leaf size: 24

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

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

✓ Solution by Mathematica

Time used: 0.044 (sec). Leaf size: 33

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

\[ y(x)\to c_1 \cos (x)+\sin (x) \left (\log \left (\sin \left (\frac {x}{2}\right )\right )-\log \left (\cos \left (\frac {x}{2}\right )\right )+c_2\right ) \]