Internal problem ID [14579]
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: 4.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime }+16 y=2 \cos \left (4 t \right )} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 27
dsolve(diff(y(t),t$2)+16*y(t)=2*cos(4*t),y(t), singsol=all)
\[ y \left (t \right ) = \frac {\left (16 c_{1} +1\right ) \cos \left (4 t \right )}{16}+\frac {\sin \left (4 t \right ) \left (t +4 c_{2} \right )}{4} \]
✓ Solution by Mathematica
Time used: 0.107 (sec). Leaf size: 31
DSolve[y''[t]+16*y[t]==2*Cos[4*t],y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to \left (\frac {1}{32}+c_1\right ) \cos (4 t)+\frac {1}{4} (t+4 c_2) \sin (4 t) \]