Internal problem ID [14583]
Book: INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton.
Fourth edition 2014. ElScAe. 2014
Section: Chapter 4. Higher Order Equations. Exercises 4.4, page 163
Problem number: 8.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime }+16 y=\cot \left (4 t \right )} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 35
dsolve(diff(y(t),t$2)+16*y(t)=cot(4*t),y(t), singsol=all)
\[ y \left (t \right ) = c_{2} \sin \left (4 t \right )+c_{1} \cos \left (4 t \right )+\frac {\sin \left (4 t \right ) \ln \left (\csc \left (4 t \right )-\cot \left (4 t \right )\right )}{16} \]
✓ Solution by Mathematica
Time used: 0.146 (sec). Leaf size: 38
DSolve[y''[t]+16*y[t]==Cot[4*t],y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to c_1 \cos (4 t)+\frac {1}{16} \sin (4 t) (\log (\sin (2 t))-\log (\cos (2 t))+16 c_2) \]