Internal problem ID [10952]
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 19.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_x]]
\[ \boxed {4 y^{\prime \prime }+40 y^{\prime }+101 y=0} \] With initial conditions \begin {align*} [y \left (0\right ) = 1, y^{\prime }\left (0\right ) = -5] \end {align*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 13
dsolve([4*diff(y(t),t$2)+40*diff(y(t),t)+101*y(t)=0,y(0) = 1, D(y)(0) = -5],y(t), singsol=all)
\[ y \left (t \right ) = {\mathrm e}^{-5 t} \cos \left (\frac {t}{2}\right ) \]
✓ Solution by Mathematica
Time used: 0.003 (sec). Leaf size: 17
DSolve[{4*y''[t]+40*y'[t]+101*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}{2}\right ) \\ \end{align*}