Internal problem ID [10955]
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 22.
ODE order: 3.
ODE degree: 1.
CAS Maple gives this as type [[_3rd_order, _missing_x]]
\[ \boxed {y^{\prime \prime \prime }+6 y^{\prime \prime }+13 y^{\prime }=0} \] With initial conditions \begin {align*} [y \left (0\right ) = 1, y^{\prime }\left (0\right ) = 1, y^{\prime \prime }\left (0\right ) = -6] \end {align*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 16
dsolve([diff(y(t),t$3)+6*diff(y(t),t$2)+13*diff(y(t),t)=0,y(0) = 1, D(y)(0) = 1, (D@@2)(y)(0) = -6],y(t), singsol=all)
\[ y \left (t \right ) = \frac {{\mathrm e}^{-3 t} \sin \left (2 t \right )}{2}+1 \]
✓ Solution by Mathematica
Time used: 0.136 (sec). Leaf size: 17
DSolve[{y'''[t]+6*y''[t]+13*y'[t]==0,{y[0]==1,y'[0]==1,y''[0]==-6}},y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to e^{-3 t} \sin (t) \cos (t)+1 \\ \end{align*}