Internal problem ID [10970]
Book: APPLIED DIFFERENTIAL EQUATIONS The Primary Course by Vladimir A. Dobrushkin.
CRC Press 2015
Section: Chapter 5.6 Laplace transform. Nonhomogeneous equations. Problems page 368
Problem number: Problem 2(i)[j].
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime }+8 y^{\prime }+20 y-\sin \left (2 t \right )=0} \] With initial conditions \begin {align*} [y \left (0\right ) = 1, y^{\prime }\left (0\right ) = -4] \end {align*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 31
dsolve([diff(y(t),t$2)+8*diff(y(t),t)+20*y(t)=sin(2*t),y(0) = 1, D(y)(0) = -4],y(t), singsol=all)
\[ y \left (t \right ) = \frac {\left (33 \,{\mathrm e}^{-4 t}-1\right ) \cos \left (2 t \right )}{32}+\frac {\sin \left (2 t \right ) \left ({\mathrm e}^{-4 t}+1\right )}{32} \]
✓ Solution by Mathematica
Time used: 0.089 (sec). Leaf size: 40
DSolve[{y''[t]+8*y'[t]+20*y[t]==Sin[2*t],{y[0]==1,y'[0]==-4}},y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to \frac {1}{32} e^{-4 t} \left (\left (e^{4 t}+1\right ) \sin (2 t)-\left (e^{4 t}-33\right ) \cos (2 t)\right ) \\ \end{align*}