Internal problem ID [10953]
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 20.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_x]]
\[ \boxed {y^{\prime \prime }+6 y^{\prime }+34 y=0} \] With initial conditions \begin {align*} [y \left (0\right ) = 3, y^{\prime }\left (0\right ) = 1] \end {align*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 22
dsolve([diff(y(t),t$2)+6*diff(y(t),t)+34*y(t)=0,y(0) = 3, D(y)(0) = 1],y(t), singsol=all)
\[ y \left (t \right ) = {\mathrm e}^{-3 t} \left (3 \cos \left (5 t \right )+2 \sin \left (5 t \right )\right ) \]
✓ Solution by Mathematica
Time used: 0.004 (sec). Leaf size: 24
DSolve[{y''[t]+6*y'[t]+34*y[t]==0,{y[0]==3,y'[0]==1}},y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to e^{-3 t} (2 \sin (5 t)+3 \cos (5 t)) \\ \end{align*}