32.9.13 problem Exercise 22.13, page 240

Internal problem ID [5987]
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 22.13, page 240
Date solved : Monday, January 27, 2025 at 01:30:16 PM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

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

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 34

dsolve(diff(y(x),x$2)+y(x)=sec(x)*csc(x),y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.024 (sec). Leaf size: 30

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

\[ y(x)\to -\sin (x) \text {arctanh}(\cos (x))+c_1 \cos (x)+c_2 \sin (x)+\cos (x) \left (-\coth ^{-1}(\sin (x))\right ) \]