32.9.10 problem Exercise 22.10, page 240

Internal problem ID [5984]
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 22.10, page 240
Date solved : Monday, January 27, 2025 at 01:30:06 PM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

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

✓ Solution by Maple

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

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

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

✓ Solution by Mathematica

Time used: 0.019 (sec). Leaf size: 24

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

\[ y(x)\to (-x+c_1) \cos (x)+\sin (x) (\log (\sin (x))+c_2) \]