Internal problem ID [10954]
Book: APPLIED DIFFERENTIAL EQUATIONS The Primary Course by Vladimir A. Dobrushkin.
CRC Press 2015
Section: Chapter 5.5 Laplace transform. Homogeneous equations. Problems page 357
Problem number: Problem 21.
ODE order: 3.
ODE degree: 1.
CAS Maple gives this as type [[_3rd_order, _missing_x]]
\[ \boxed {y^{\prime \prime \prime }+8 y^{\prime \prime }+16 y^{\prime }=0} \] With initial conditions \begin {align*} [y \left (0\right ) = 1, y^{\prime }\left (0\right ) = 1, y^{\prime \prime }\left (0\right ) = -8] \end {align*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 12
dsolve([diff(y(t),t$3)+8*diff(y(t),t$2)+16*diff(y(t),t)=0,y(0) = 1, D(y)(0) = 1, (D@@2)(y)(0) = -8],y(t), singsol=all)
\[ y \left (t \right ) = t \,{\mathrm e}^{-4 t}+1 \]
✓ Solution by Mathematica
Time used: 0.022 (sec). Leaf size: 14
DSolve[{y'''[t]+8*y''[t]+16*y'[t]==0,{y[0]==1,y'[0]==1,y''[0]==-8}},y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to e^{-4 t} t+1 \\ \end{align*}