Internal problem ID [2858]
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 20.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime }-y=8 \sin \left (t \right )-6 \cos \left (t \right )} \] With initial conditions \begin {align*} [y \left (0\right ) = 2, y^{\prime }\left (0\right ) = -1] \end {align*}
✓ Solution by Maple
Time used: 0.031 (sec). Leaf size: 21
dsolve([diff(y(t),t$2)-y(t)=8*sin(t)-6*cos(t),y(0) = 2, D(y)(0) = -1],y(t), singsol=all)
\[ y \left (t \right ) = -2 \,{\mathrm e}^{-t}+{\mathrm e}^{t}-4 \sin \left (t \right )+3 \cos \left (t \right ) \]
✓ Solution by Mathematica
Time used: 0.02 (sec). Leaf size: 24
DSolve[{y''[t]-y[t]==8*Sin[t]-6*Cos[t],{y[0]==2,y'[0]==-1}},y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to -2 e^{-t}+e^t-4 \sin (t)+3 \cos (t) \]