90.13.7 problem 7

Internal problem ID [25219]
Book : Ordinary Differential Equations. By William Adkins and Mark G Davidson. Springer. NY. 2010. ISBN 978-1-4614-3617-1
Section : Chapter 3. Second Order Constant Coefficient Linear Differential Equations. Exercises at page 235
Problem number : 7
Date solved : Thursday, October 02, 2025 at 11:59:03 PM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} y^{\prime \prime }+2 y^{\prime }+5 y&=0 \end{align*}

✓ Maple. Time used: 0.000 (sec). Leaf size: 22

ode:=diff(diff(y(t),t),t)+2*diff(y(t),t)+5*y(t) = 0; 
dsolve(ode,y(t), singsol=all);
 

\[ y = {\mathrm e}^{-t} \left (c_1 \sin \left (2 t \right )+c_2 \cos \left (2 t \right )\right ) \]

✓ Mathematica. Time used: 0.011 (sec). Leaf size: 26

ode=D[y[t],{t,2}]+2*D[y[t],t]+5*y[t]==0; 
ic={}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\begin{align*} y(t)&\to e^{-t} (c_2 \cos (2 t)+c_1 \sin (2 t)) \end{align*}

✓ Sympy. Time used: 0.089 (sec). Leaf size: 19

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(5*y(t) + 2*Derivative(y(t), t) + Derivative(y(t), (t, 2)),0) 
ics = {} 
dsolve(ode,func=y(t),ics=ics)
 

\[ y{\left (t \right )} = \left (C_{1} \sin {\left (2 t \right )} + C_{2} \cos {\left (2 t \right )}\right ) e^{- t} \]