Internal problem ID [13779]
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).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime }+4 y=\csc \left (2 x \right )} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 35
dsolve(diff(y(x),x$2)+4*y(x)=csc(2*x),y(x), singsol=all)
\[ y \left (x \right ) = -\frac {\ln \left (\csc \left (2 x \right )\right ) \sin \left (2 x \right )}{4}+\frac {\left (-2 x +4 c_{1} \right ) \cos \left (2 x \right )}{4}+c_{2} \sin \left (2 x \right ) \]
✓ Solution by Mathematica
Time used: 0.031 (sec). Leaf size: 37
DSolve[y''[x]+4*y[x]==Csc[2*x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \left (-\frac {x}{2}+c_1\right ) \cos (2 x)+\frac {1}{4} \sin (2 x) (\log (\sin (2 x))+4 c_2) \]