73.16.3 problem 24.1 (c)

Internal problem ID [15515]
Book : Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell. second edition. CRC Press. FL, USA. 2020
Section : Chapter 24. Variation of parameters. Additional exercises page 444
Problem number : 24.1 (c)
Date solved : Tuesday, January 28, 2025 at 08:00:45 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }+4 y&=\csc \left (2 x \right ) \end{align*}

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 35

dsolve(diff(y(x),x$2)+4*y(x)=csc(2*x),y(x), singsol=all)
 

\[ y = -\frac {\ln \left (\csc \left (2 x \right )\right ) \sin \left (2 x \right )}{4}+\frac {\left (-2 x +4 c_{1} \right ) \cos \left (2 x \right )}{4}+\sin \left (2 x \right ) c_{2} \]

✓ Solution by Mathematica

Time used: 0.029 (sec). Leaf size: 37

DSolve[D[y[x],{x,2}]+4*y[x]==Csc[2*x],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \left (-\frac {x}{2}+c_1\right ) \cos (2 x)+\frac {1}{4} \sin (2 x) (\log (\sin (2 x))+4 c_2) \]