Internal problem ID [2352]
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 23.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
Solve \begin {gather*} \boxed {y^{\prime \prime }+5 y^{\prime }+4 y-20 \sin \left (2 t \right )=0} \end {gather*} With initial conditions \begin {align*} [y \relax (0) = 1, y^{\prime }\relax (0) = -2] \end {align*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 23
dsolve([diff(y(t),t$2)+5*diff(y(t),t)+4*y(t)=20*sin(2*t),y(0) = 1, D(y)(0) = -2],y(t), singsol=all)
\[ y \relax (t ) = \frac {10 \,{\mathrm e}^{-t}}{3}-\frac {{\mathrm e}^{-4 t}}{3}-2 \cos \left (2 t \right ) \]
✓ Solution by Mathematica
Time used: 0.004 (sec). Leaf size: 30
DSolve[{y''[t]+5*y'[t]+4*y[t]==20*Sin[2*t],{y[0]==1,y'[0]==-2}},y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to \frac {1}{3} e^{-4 t} \left (10 e^{3 t}-1\right )-2 \cos (2 t) \\ \end{align*}