20.21.19 problem Problem 19

Internal problem ID [3946]
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 19
Date solved : Monday, January 27, 2025 at 08:04:51 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }-9 y&=13 \sin \left (2 t \right ) \end{align*}

Using Laplace method With initial conditions

\begin{align*} y \left (0\right )&=3\\ y^{\prime }\left (0\right )&=1 \end{align*}

✓ Solution by Maple

Time used: 2.638 (sec). Leaf size: 21

dsolve([diff(y(t),t$2)-9*y(t)=13*sin(2*t),y(0) = 3, D(y)(0) = 1],y(t), singsol=all)
 

\[ y = {\mathrm e}^{-3 t}+2 \,{\mathrm e}^{3 t}-\sin \left (2 t \right ) \]

✓ Solution by Mathematica

Time used: 0.018 (sec). Leaf size: 24

DSolve[{D[y[t],{t,2}]-9*y[t]==13*Sin[2*t],{y[0]==3,Derivative[1][y][0] ==1}},y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to e^{-3 t}+2 e^{3 t}-\sin (2 t) \]