67.3.17 problem Problem 18

Internal problem ID [14035]
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
Date solved : Tuesday, January 28, 2025 at 06:13:04 AM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} 2 y^{\prime \prime }+20 y^{\prime }+51 y&=0 \end{align*}

Using Laplace method With initial conditions

\begin{align*} y \left (0\right )&=1\\ y^{\prime }\left (0\right )&=-5 \end{align*}

✓ Solution by Maple

Time used: 8.912 (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)
 

\[ y = {\mathrm e}^{-5 t} \cos \left (\frac {\sqrt {2}\, t}{2}\right ) \]

✓ Solution by Mathematica

Time used: 0.025 (sec). Leaf size: 19

DSolve[{2*D[y[t],{t,2}]+20*D[y[t],t]+51*y[t]==0,{y[0]==1,Derivative[1][y][0] ==-5}},y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to e^{-5 t} \cos \left (\frac {t}{\sqrt {2}}\right ) \]