Internal problem ID [10951]
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 18.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_x]]
\[ \boxed {2 y^{\prime \prime }+20 y^{\prime }+51 y=0} \] With initial conditions \begin {align*} [y \left (0\right ) = 1, y^{\prime }\left (0\right ) = -5] \end {align*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 16
dsolve([2*diff(y(t),t$2)+20*diff(y(t),t)+51*y(t)=0,y(0) = 1, D(y)(0) = -5],y(t), singsol=all)
\[ y \left (t \right ) = {\mathrm e}^{-5 t} \cos \left (\frac {\sqrt {2}\, t}{2}\right ) \]
✓ Solution by Mathematica
Time used: 0.004 (sec). Leaf size: 19
DSolve[{2*y''[t]+20*y'[t]+51*y[t]==0,{y[0]==1,y'[0]==-5}},y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to e^{-5 t} \cos \left (\frac {t}{\sqrt {2}}\right ) \\ \end{align*}