68.10.25 problem 25

Internal problem ID [17517]
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 : 25
Date solved : Thursday, October 02, 2025 at 02:25:00 PM
CAS classification : [[_2nd_order, _missing_x]]

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

With initial conditions

\begin{align*} y \left (0\right )&=1 \\ y^{\prime }\left (0\right )&=3 \\ \end{align*}

✓ Maple. Time used: 0.048 (sec). Leaf size: 14

ode:=diff(diff(y(t),t),t)+4*diff(y(t),t)+4*y(t) = 0; 
ic:=[y(0) = 1, D(y)(0) = 3]; 
dsolve([ode,op(ic)],y(t), singsol=all);
 

\[ y = {\mathrm e}^{-2 t} \left (1+5 t \right ) \]

✓ Mathematica. Time used: 0.01 (sec). Leaf size: 16

ode=D[y[t],{t,2}]+4*D[y[t],t]+4*y[t]==0; 
ic={y[0]==1,Derivative[1][y][0] ==3}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\begin{align*} y(t)&\to e^{-2 t} (5 t+1) \end{align*}

✓ Sympy. Time used: 0.096 (sec). Leaf size: 12

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(4*y(t) + 4*Derivative(y(t), t) + Derivative(y(t), (t, 2)),0) 
ics = {y(0): 1, Subs(Derivative(y(t), t), t, 0): 3} 
dsolve(ode,func=y(t),ics=ics)
 

\[ y{\left (t \right )} = \left (5 t + 1\right ) e^{- 2 t} \]