Internal problem ID [10957]
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 24.
ODE order: 3.
ODE degree: 1.
CAS Maple gives this as type [[_3rd_order, _missing_x]]
\[ \boxed {y^{\prime \prime \prime }+4 y^{\prime \prime }+29 y^{\prime }=0} \] With initial conditions \begin {align*} [y \left (0\right ) = 1, y^{\prime }\left (0\right ) = 5, y^{\prime \prime }\left (0\right ) = -20] \end {align*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 15
dsolve([diff(y(t),t$3)+4*diff(y(t),t$2)+29*diff(y(t),t)=0,y(0) = 1, D(y)(0) = 5, (D@@2)(y)(0) = -20],y(t), singsol=all)
\[ y \left (t \right ) = {\mathrm e}^{-2 t} \sin \left (5 t \right )+1 \]
✓ Solution by Mathematica
Time used: 0.158 (sec). Leaf size: 30
DSolve[{y'''[t]+4*y''[t]-20*y'[t]==0,{y[0]==1,y'[0]==5,y''[0]==-20}},y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to \frac {5 e^{-2 t} \sinh \left (2 \sqrt {6} t\right )}{2 \sqrt {6}}+1 \\ \end{align*}