74.10.27 problem 27

Internal problem ID [16153]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 4. Higher Order Equations. Exercises 4.2, page 147
Problem number : 27
Date solved : Thursday, March 13, 2025 at 07:53:40 AM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} y^{\prime \prime }+4 y^{\prime }+20 y&=0 \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=2\\ y^{\prime }\left (0\right )&=0 \end{align*}

✓ Maple. Time used: 0.016 (sec). Leaf size: 20

ode:=diff(diff(y(t),t),t)+4*diff(y(t),t)+20*y(t) = 0; 
ic:=y(0) = 2, D(y)(0) = 0; 
dsolve([ode,ic],y(t), singsol=all);
 

\[ y = {\mathrm e}^{-2 t} \left (\sin \left (4 t \right )+2 \cos \left (4 t \right )\right ) \]

✓ Mathematica. Time used: 0.019 (sec). Leaf size: 22

ode=D[y[t],{t,2}]+4*D[y[t],t]+20*y[t]==0; 
ic={y[0]==2,Derivative[1][y][0] ==0}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\[ y(t)\to e^{-2 t} (\sin (4 t)+2 \cos (4 t)) \]

✓ Sympy. Time used: 0.173 (sec). Leaf size: 19

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(20*y(t) + 4*Derivative(y(t), t) + Derivative(y(t), (t, 2)),0) 
ics = {y(0): 2, Subs(Derivative(y(t), t), t, 0): 0} 
dsolve(ode,func=y(t),ics=ics)
 

\[ y{\left (t \right )} = \left (\sin {\left (4 t \right )} + 2 \cos {\left (4 t \right )}\right ) e^{- 2 t} \]