30.12.11 problem 11

Internal problem ID [7603]
Book : Fundamentals of Differential Equations. By Nagle, Saff and Snider. 9th edition. Boston. Pearson 2018.
Section : Chapter 4, Linear Second-Order Equations. EXERCISES 4.2 at page 164
Problem number : 11
Date solved : Tuesday, September 30, 2025 at 04:54:49 PM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} 4 w^{\prime \prime }+20 w^{\prime }+25 w&=0 \end{align*}

✓ Maple. Time used: 0.001 (sec). Leaf size: 14

ode:=4*diff(diff(w(t),t),t)+20*diff(w(t),t)+25*w(t) = 0; 
dsolve(ode,w(t), singsol=all);
 

\[ w = {\mathrm e}^{-\frac {5 t}{2}} \left (c_2 t +c_1 \right ) \]

✓ Mathematica. Time used: 0.007 (sec). Leaf size: 20

ode=4*D[w[t],{t,2}]+20*D[w[t],t]+25*w[t]==0; 
ic={}; 
DSolve[{ode,ic},w[t],t,IncludeSingularSolutions->True]
 

\begin{align*} w(t)&\to e^{-5 t/2} (c_2 t+c_1) \end{align*}

✓ Sympy. Time used: 0.096 (sec). Leaf size: 14

from sympy import * 
t = symbols("t") 
w = Function("w") 
ode = Eq(25*w(t) + 20*Derivative(w(t), t) + 4*Derivative(w(t), (t, 2)),0) 
ics = {} 
dsolve(ode,func=w(t),ics=ics)
 

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