20.21.27 problem Problem 27

Internal problem ID [3954]
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 27
Date solved : Monday, January 27, 2025 at 08:04:57 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }+9 y&=7 \sin \left (4 t \right )+14 \cos \left (4 t \right ) \end{align*}

Using Laplace method With initial conditions

\begin{align*} y \left (0\right )&=1\\ y^{\prime }\left (0\right )&=2 \end{align*}

✓ Solution by Maple

Time used: 3.550 (sec). Leaf size: 29

dsolve([diff(y(t),t$2)+9*y(t)=7*sin(4*t)+14*cos(4*t),y(0) = 1, D(y)(0) = 2],y(t), singsol=all)
 

\[ y = -2 \cos \left (4 t \right )-\sin \left (4 t \right )+3 \cos \left (3 t \right )+2 \sin \left (3 t \right ) \]

✓ Solution by Mathematica

Time used: 0.024 (sec). Leaf size: 49

DSolve[{D[y[t],{t,2}]+8*y[t]==7*Sin[4*t]+14*Cos[4*t],{y[0]==1,Derivative[1][y][0] ==2}},y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to \frac {1}{8} \left (-7 \sin (4 t)+11 \sqrt {2} \sin \left (2 \sqrt {2} t\right )-14 \cos (4 t)+22 \cos \left (2 \sqrt {2} t\right )\right ) \]