13.26 problem Problem 26

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]]

Solve \begin {gather*} \boxed {y^{\prime \prime }+y-6 \cos \left (2 t \right )=0} \end {gather*} With initial conditions \begin {align*} [y \relax (0) = 0, y^{\prime }\relax (0) = 2] \end {align*}

Solution by Maple

Time used: 0.016 (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)
 

\[ y \relax (t ) = 2 \sin \relax (t )+2 \cos \relax (t )-4 \left (\cos ^{2}\relax (t )\right )+2 \]

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*}