Internal problem ID [14611]
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: 36.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime }+16 y=\tan \left (2 t \right )} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 56
dsolve(diff(y(t),t$2)+16*y(t)=tan(2*t),y(t), singsol=all)
\[ y \left (t \right ) = \frac {\sin \left (2 t \right ) \cos \left (2 t \right ) \ln \left (\cos \left (2 t \right )\right )}{4}+\frac {\left (-t +4 c_{1} \right ) \cos \left (2 t \right )^{2}}{2}+\frac {\sin \left (2 t \right ) \left (16 c_{2} -1\right ) \cos \left (2 t \right )}{8}+\frac {t}{4}-c_{1} \]
✓ Solution by Mathematica
Time used: 0.057 (sec). Leaf size: 40
DSolve[y''[t]+16*y[t]==Tan[2*t],y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to \left (-\frac {t}{4}+c_1\right ) \cos (4 t)+\frac {1}{16} \sin (4 t) (2 \log (\cos (2 t))-1+16 c_2) \]