67.3.19 problem Problem 20

Internal problem ID [14037]
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
Date solved : Tuesday, January 28, 2025 at 06:13:05 AM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} y^{\prime \prime }+6 y^{\prime }+34 y&=0 \end{align*}

Using Laplace method With initial conditions

\begin{align*} y \left (0\right )&=3\\ y^{\prime }\left (0\right )&=1 \end{align*}

✓ Solution by Maple

Time used: 8.743 (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)
 

\[ y = {\mathrm e}^{-3 t} \left (3 \cos \left (5 t \right )+2 \sin \left (5 t \right )\right ) \]

✓ Solution by Mathematica

Time used: 0.018 (sec). Leaf size: 24

DSolve[{D[y[t],{t,2}]+6*D[y[t],t]+34*y[t]==0,{y[0]==3,Derivative[1][y][0] ==1}},y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to e^{-3 t} (2 \sin (5 t)+3 \cos (5 t)) \]