Internal problem ID [2863]
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 25.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime }+4 y=9 \sin \left (t \right )} \] With initial conditions \begin {align*} [y \left (0\right ) = 1, y^{\prime }\left (0\right ) = -1] \end {align*}
✓ Solution by Maple
Time used: 2.047 (sec). Leaf size: 19
dsolve([diff(y(t),t$2)+4*y(t)=9*sin(t),y(0) = 1, D(y)(0) = -1],y(t), singsol=all)
\[ y \left (t \right ) = \cos \left (2 t \right )-2 \sin \left (2 t \right )+3 \sin \left (t \right ) \]
✓ Solution by Mathematica
Time used: 0.019 (sec). Leaf size: 20
DSolve[{y''[t]+4*y[t]==9*Sin[t],{y[0]==1,y'[0]==-1}},y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to 3 \sin (t)-2 \sin (2 t)+\cos (2 t) \]