Internal problem ID [2355]
Book: Differential equations and linear algebra, Stephen W. Goode and Scott A Annin. Fourth edition,
2015
Section: Chapter 10, The Laplace Transform and Some Elementary Applications. Exercises for 10.4.
page 689
Problem number: Problem 26.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime }+y-6 \cos \left (2 t \right )=0} \] With initial conditions \begin {align*} [y \left (0\right ) = 0, y^{\prime }\left (0\right ) = 2] \end {align*}
✓ Solution by Maple
Time used: 0.032 (sec). Leaf size: 19
dsolve([diff(y(t),t$2)+y(t)=6*cos(2*t),y(0) = 0, D(y)(0) = 2],y(t), singsol=all)
\[ y \left (t \right ) = 2 \sin \left (t \right )+2 \cos \left (t \right )-2 \cos \left (2 t \right ) \]
✓ Solution by Mathematica
Time used: 0.005 (sec). Leaf size: 18
DSolve[{y''[t]+y[t]==6*Cos[2*t],{y[0]==0,y'[0]==2}},y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to 2 (\sin (t)+\cos (t)-\cos (2 t)) \\ \end{align*}