Internal problem ID [14614]
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: 39.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime }+4 y=\sec \left (2 t \right ) \tan \left (2 t \right )} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 38
dsolve(diff(y(t),t$2)+4*y(t)=sec(2*t)*tan(2*t),y(t), singsol=all)
\[ y \left (t \right ) = \frac {\ln \left (\sec \left (2 t \right )\right ) \sin \left (2 t \right )}{4}+\frac {\left (4 c_{2} -1\right ) \sin \left (2 t \right )}{4}+\frac {\cos \left (2 t \right ) \left (2 c_{1} +t \right )}{2} \]
✓ Solution by Mathematica
Time used: 0.058 (sec). Leaf size: 46
DSolve[y''[t]+4*y[t]==Sec[2*t]*Tan[2*t],y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to \frac {1}{4} (\cos (2 t) \arctan (\tan (2 t))+4 c_1 \cos (2 t)+\sin (2 t) (-\log (\cos (2 t))-1+4 c_2)) \]