Internal problem ID [14616]
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: 41.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime }+4 y=\sec \left (2 t \right )^{2}} \] With initial conditions \begin {align*} [y \left (0\right ) = 0, y^{\prime }\left (0\right ) = 1] \end {align*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 34
dsolve([diff(y(t),t$2)+4*y(t)=sec(2*t)^2,y(0) = 0, D(y)(0) = 1],y(t), singsol=all)
\[ y \left (t \right ) = \frac {\sin \left (2 t \right )}{2}+\frac {\cos \left (2 t \right )}{4}-\frac {1}{4}+\frac {\ln \left (\sec \left (2 t \right )+\tan \left (2 t \right )\right ) \sin \left (2 t \right )}{4} \]
✓ Solution by Mathematica
Time used: 0.101 (sec). Leaf size: 35
DSolve[{y''[t]+4*y[t]==Sec[2*t]^2,{y[0]==0,y'[0]==1}},y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to \frac {1}{4} \sin (t) \left (-2 \sin (t)+(4-i \pi ) \cos (t)+2 \cos (t) \coth ^{-1}(\sin (2 t))\right ) \]