67.3.18 problem Problem 19

Internal problem ID [14036]
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
Date solved : Tuesday, January 28, 2025 at 06:13:05 AM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} 4 y^{\prime \prime }+40 y^{\prime }+101 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: 8.919 (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)
 

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

✓ Solution by Mathematica

Time used: 0.019 (sec). Leaf size: 17

DSolve[{4*D[y[t],{t,2}]+40*D[y[t],t]+101*y[t]==0,{y[0]==1,Derivative[1][y][0] ==-5}},y[t],t,IncludeSingularSolutions -> True]
 

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