87.12.24 problem 27

Internal problem ID [23472]
Book : Ordinary differential equations with modern applications. Ladas, G. E. and Finizio, N. Wadsworth Publishing. California. 1978. ISBN 0-534-00552-7. QA372.F56
Section : Chapter 2. Linear differential equations. Exercise at page 93
Problem number : 27
Date solved : Thursday, October 02, 2025 at 09:42:11 PM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} y^{\prime \prime }+20 y^{\prime }+64 y&=0 \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 17

ode:=diff(diff(y(t),t),t)+20*diff(y(t),t)+64*y(t) = 0; 
dsolve(ode,y(t), singsol=all);
 

\[ y = c_1 \,{\mathrm e}^{-4 t}+c_2 \,{\mathrm e}^{-16 t} \]

✓ Mathematica. Time used: 0.013 (sec). Leaf size: 22

ode=D[y[t],{t,2}]+20*D[y[t],t]+64*y[t]==0; 
ic={}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\begin{align*} y(t)&\to e^{-16 t} \left (c_2 e^{12 t}+c_1\right ) \end{align*}

✓ Sympy. Time used: 0.108 (sec). Leaf size: 15

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(64*y(t) + 20*Derivative(y(t), t) + Derivative(y(t), (t, 2)),0) 
ics = {} 
dsolve(ode,func=y(t),ics=ics)
 

\[ y{\left (t \right )} = \left (C_{1} + C_{2} e^{- 12 t}\right ) e^{- 4 t} \]