Internal problem ID [14610]
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: 35.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime }+4 y=\tan \left (2 t \right )} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 33
dsolve(diff(y(t),t$2)+4*y(t)=tan(2*t),y(t), singsol=all)
\[ y \left (t \right ) = \sin \left (2 t \right ) c_{2} +\cos \left (2 t \right ) c_{1} -\frac {\cos \left (2 t \right ) \ln \left (\sec \left (2 t \right )+\tan \left (2 t \right )\right )}{4} \]
✓ Solution by Mathematica
Time used: 0.046 (sec). Leaf size: 40
DSolve[y''[t]+4*y[t]==Tan[2*t],y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to -\frac {1}{4} \cos (2 t) \text {arctanh}(\sin (2 t))+c_1 \cos (2 t)+\frac {1}{4} (-1+4 c_2) \sin (2 t) \]