Internal problem ID [10944]
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 11.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_x]]
\[ \boxed {y^{\prime \prime }+4 y^{\prime }+13 y=0} \] With initial conditions \begin {align*} [y \left (0\right ) = 1, y^{\prime }\left (0\right ) = -6] \end {align*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 24
dsolve([diff(y(t),t$2)+4*diff(y(t),t)+13*y(t)=0,y(0) = 1, D(y)(0) = -6],y(t), singsol=all)
\[ y \left (t \right ) = -\frac {{\mathrm e}^{-2 t} \left (4 \sin \left (3 t \right )-3 \cos \left (3 t \right )\right )}{3} \]
✓ Solution by Mathematica
Time used: 0.003 (sec). Leaf size: 27
DSolve[{y''[t]+4*y'[t]+13*y[t]==0,{y[0]==1,y'[0]==-6}},y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to \frac {1}{3} e^{-2 t} (3 \cos (3 t)-4 \sin (3 t)) \\ \end{align*}