Internal problem ID [14525]
Book: INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton.
Fourth edition 2014. ElScAe. 2014
Section: Chapter 4. Higher Order Equations. Exercises 4.3, page 156
Problem number: 19.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime }+y=\cos \left (2 t \right )} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 19
dsolve(diff(y(t),t$2)+y(t)=cos(2*t),y(t), singsol=all)
\[ y \left (t \right ) = \sin \left (t \right ) c_{2} +\cos \left (t \right ) c_{1} -\frac {\cos \left (2 t \right )}{3} \]
✓ Solution by Mathematica
Time used: 0.106 (sec). Leaf size: 24
DSolve[y''[t]+y[t]==Cos[2*t],y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to -\frac {1}{3} \cos (2 t)+c_1 \cos (t)+c_2 \sin (t) \]