Internal problem ID [2348]
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.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime }-9 y-13 \sin \left (2 t \right )=0} \] With initial conditions \begin {align*} [y \left (0\right ) = 3, y^{\prime }\left (0\right ) = 1] \end {align*}
✓ Solution by Maple
Time used: 0.015 (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)
\[ y \left (t \right ) = 2 \,{\mathrm e}^{3 t}+{\mathrm e}^{-3 t}-\sin \left (2 t \right ) \]
✓ Solution by Mathematica
Time used: 0.006 (sec). Leaf size: 22
DSolve[{y''[t]-9*y[t]==13*Sin[2*t],{y[0]==3,y'[0]==1}},y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to -\sin (2 t)+\sinh (3 t)+3 \cosh (3 t) \\ \end{align*}