Internal problem ID [10963]
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(c).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {4 y^{\prime \prime }+5 y^{\prime }+4 y-3 \,{\mathrm e}^{-t}=0} \] With initial conditions \begin {align*} [y \left (0\right ) = -1, y^{\prime }\left (0\right ) = 1] \end {align*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 38
dsolve([4*diff(y(t),t$2)+5*diff(y(t),t)+4*y(t)=3*exp(-t),y(0) = -1, D(y)(0) = 1],y(t), singsol=all)
\[ y \left (t \right ) = \frac {2 \,{\mathrm e}^{-\frac {5 t}{8}} \sqrt {39}\, \sin \left (\frac {\sqrt {39}\, t}{8}\right )}{13}-2 \,{\mathrm e}^{-\frac {5 t}{8}} \cos \left (\frac {\sqrt {39}\, t}{8}\right )+{\mathrm e}^{-t} \]
✓ Solution by Mathematica
Time used: 0.009 (sec). Leaf size: 53
DSolve[{4*y''[t]+5*y'[t]+4*y[t]==3*Exp[-t],{y[0]==-1,y'[0]==1}},y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to e^{-t}+\frac {2}{13} e^{-5 t/8} \left (\sqrt {39} \sin \left (\frac {\sqrt {39} t}{8}\right )-13 \cos \left (\frac {\sqrt {39} t}{8}\right )\right ) \\ \end{align*}