50.11.8 problem 2(b)

Internal problem ID [7992]
Book : Differential Equations: Theory, Technique, and Practice by George Simmons, Steven Krantz. McGraw-Hill NY. 2007. 1st Edition.
Section : Chapter 2. Second-Order Linear Equations. Section 2.3. THE METHOD OF VARIATION OF PARAMETERS. Page 71
Problem number : 2(b)
Date solved : Monday, January 27, 2025 at 03:36:02 PM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }+y&=\cot \left (x \right )^{2} \end{align*}

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 26

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

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

✓ Solution by Mathematica

Time used: 0.045 (sec). Leaf size: 34

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

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