68.18.33 problem 39

Internal problem ID [17877]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 4. Higher Order Equations. Chapter 4 review exercises, page 219
Problem number : 39
Date solved : Thursday, October 02, 2025 at 02:29:07 PM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} y^{\prime \prime }+10 y^{\prime }+16 y&=0 \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=0 \\ y^{\prime }\left (0\right )&=4 \\ \end{align*}

✓ Maple. Time used: 0.050 (sec). Leaf size: 17

ode:=diff(diff(y(t),t),t)+10*diff(y(t),t)+16*y(t) = 0; 
ic:=[y(0) = 0, D(y)(0) = 4]; 
dsolve([ode,op(ic)],y(t), singsol=all);
 

\[ y = -\frac {2 \,{\mathrm e}^{-8 t}}{3}+\frac {2 \,{\mathrm e}^{-2 t}}{3} \]

✓ Mathematica. Time used: 0.009 (sec). Leaf size: 21

ode=D[y[t],{t,2}]+10*D[y[t],t]+16*y[t]==0; 
ic={y[0]==0,Derivative[1][y][0] ==4}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\begin{align*} y(t)&\to \frac {2}{3} e^{-8 t} \left (e^{6 t}-1\right ) \end{align*}

✓ Sympy. Time used: 0.116 (sec). Leaf size: 19

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(16*y(t) + 10*Derivative(y(t), t) + Derivative(y(t), (t, 2)),0) 
ics = {y(0): 0, Subs(Derivative(y(t), t), t, 0): 4} 
dsolve(ode,func=y(t),ics=ics)
 

\[ y{\left (t \right )} = \left (\frac {2}{3} - \frac {2 e^{- 6 t}}{3}\right ) e^{- 2 t} \]