Internal problem ID [2859]
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 21.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime }-y^{\prime }-2 y=10 \cos \left (t \right )} \] With initial conditions \begin {align*} [y \left (0\right ) = 0, y^{\prime }\left (0\right ) = -1] \end {align*}
✓ Solution by Maple
Time used: 1.891 (sec). Leaf size: 23
dsolve([diff(y(t),t$2)-diff(y(t),t)-2*y(t)=10*cos(t),y(0) = 0, D(y)(0) = -1],y(t), singsol=all)
\[ y \left (t \right ) = 2 \,{\mathrm e}^{-t}+{\mathrm e}^{2 t}-3 \cos \left (t \right )-\sin \left (t \right ) \]
✓ Solution by Mathematica
Time used: 0.02 (sec). Leaf size: 26
DSolve[{y''[t]-y'[t]-2*y[t]==10*Cos[t],{y[0]==0,y'[0]==-1}},y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to 2 e^{-t}+e^{2 t}-\sin (t)-3 \cos (t) \]