Internal problem ID [2350]
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]]
Solve \begin {gather*} \boxed {y^{\prime \prime }-y^{\prime }-2 y-10 \cos \relax (t )=0} \end {gather*} With initial conditions \begin {align*} [y \relax (0) = 0, y^{\prime }\relax (0) = -1] \end {align*}
✓ Solution by Maple
Time used: 0.016 (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)
\[ y \relax (t ) = {\mathrm e}^{2 t}+2 \,{\mathrm e}^{-t}-3 \cos \relax (t )-\sin \relax (t ) \]
✓ Solution by Mathematica
Time used: 0.007 (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]
\begin{align*} y(t)\to 2 e^{-t}+e^{2 t}-\sin (t)-3 \cos (t) \\ \end{align*}