67.3.19 problem Problem 20

Internal problem ID [13958]
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 : Wednesday, March 05, 2025 at 10:24:15 PM
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*}

✓ Maple. Time used: 8.743 (sec). Leaf size: 22

ode:=diff(diff(y(t),t),t)+6*diff(y(t),t)+34*y(t) = 0; 
ic:=y(0) = 3, D(y)(0) = 1; 
dsolve([ode,ic],y(t),method='laplace');
 

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

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

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

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

✓ Sympy. Time used: 0.191 (sec). Leaf size: 20

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(34*y(t) + 6*Derivative(y(t), t) + Derivative(y(t), (t, 2)),0) 
ics = {y(0): 3, Subs(Derivative(y(t), t), t, 0): 1} 
dsolve(ode,func=y(t),ics=ics)
 

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