Internal problem ID [2857]
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]]
\[ \boxed {y^{\prime \prime }-9 y=13 \sin \left (2 t \right )} \] With initial conditions \begin {align*} [y \left (0\right ) = 3, y^{\prime }\left (0\right ) = 1] \end {align*}
✓ Solution by Maple
Time used: 2.75 (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)
\[ y \left (t \right ) = -\sin \left (2 t \right )+2 \,{\mathrm e}^{3 t}+{\mathrm e}^{-3 t} \]
✓ Solution by Mathematica
Time used: 0.019 (sec). Leaf size: 24
DSolve[{y''[t]-9*y[t]==13*Sin[2*t],{y[0]==3,y'[0]==1}},y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to e^{-3 t}+2 e^{3 t}-\sin (2 t) \]