Internal problem ID [2347]
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 18.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
Solve \begin {gather*} \boxed {y^{\prime \prime }-y-6 \cos \relax (t )=0} \end {gather*} With initial conditions \begin {align*} [y \relax (0) = 0, y^{\prime }\relax (0) = 4] \end {align*}
✓ Solution by Maple
Time used: 0.017 (sec). Leaf size: 19
dsolve([diff(y(t),t$2)-y(t)=6*cos(t),y(0) = 0, D(y)(0) = 4],y(t), singsol=all)
\[ y \relax (t ) = -\frac {{\mathrm e}^{-t}}{2}+\frac {7 \,{\mathrm e}^{t}}{2}-3 \cos \relax (t ) \]
✓ Solution by Mathematica
Time used: 0.023 (sec). Leaf size: 18
DSolve[{y''[t]-y[t]==6*Cos[t],{y[0]==0,y'[0]==4}},y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to -3 \cos (t)+4 \sinh (t)+3 \cosh (t) \\ \end{align*}