Internal problem ID [14619]
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: 44.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime }+4 y=\sec \left (2 t \right )+\tan \left (2 t \right )} \] With initial conditions \begin {align*} [y \left (0\right ) = 1, y^{\prime }\left (0\right ) = 0] \end {align*}
✓ Solution by Maple
Time used: 0.047 (sec). Leaf size: 42
dsolve([diff(y(t),t$2)+4*y(t)=sec(2*t)+tan(2*t),y(0) = 1, D(y)(0) = 0],y(t), singsol=all)
\[ y \left (t \right ) = \frac {\sin \left (2 t \right )}{4}-\frac {i \cos \left (2 t \right ) \pi }{4}+\cos \left (2 t \right )+\frac {t \sin \left (2 t \right )}{2}+\frac {\cos \left (2 t \right ) \ln \left (\sin \left (2 t \right )-1\right )}{4} \]
✓ Solution by Mathematica
Time used: 0.509 (sec). Leaf size: 36
DSolve[{y''[t]+4*y[t]==Sec[2*t]+Tan[2*t],{y[0]==1,y'[0]==0}},y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to \frac {1}{4} ((2 t+1) \sin (2 t)+2 \cos (2 t) (\log (\cos (t)-\sin (t))+2)) \]