20.21.26 problem Problem 26

Internal problem ID [3953]
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
Date solved : Monday, January 27, 2025 at 08:04:56 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }+y&=6 \cos \left (2 t \right ) \end{align*}

Using Laplace method With initial conditions

\begin{align*} y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=2 \end{align*}

✓ Solution by Maple

Time used: 2.822 (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)
 

\[ y = 2 \cos \left (t \right )+2 \sin \left (t \right )-2 \cos \left (2 t \right ) \]

✓ Solution by Mathematica

Time used: 0.016 (sec). Leaf size: 18

DSolve[{D[y[t],{t,2}]+y[t]==6*Cos[2*t],{y[0]==0,Derivative[1][y][0] ==2}},y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to 2 (\sin (t)+\cos (t)-\cos (2 t)) \]