Internal problem ID [2856]
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]]
\[ \boxed {y^{\prime \prime }-y=6 \cos \left (t \right )} \] With initial conditions \begin {align*} [y \left (0\right ) = 0, y^{\prime }\left (0\right ) = 4] \end {align*}
✓ Solution by Maple
Time used: 1.859 (sec). Leaf size: 17
dsolve([diff(y(t),t$2)-y(t)=6*cos(t),y(0) = 0, D(y)(0) = 4],y(t), singsol=all)
\[ y \left (t \right ) = 4 \sinh \left (t \right )-3 \cos \left (t \right )+3 \cosh \left (t \right ) \]
✓ Solution by Mathematica
Time used: 0.018 (sec). Leaf size: 26
DSolve[{y''[t]-y[t]==6*Cos[t],{y[0]==0,y'[0]==4}},y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to \frac {1}{2} \left (-e^{-t}+7 e^t-6 \cos (t)\right ) \]