74.9.17 problem 28

Internal problem ID [16114]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 4. Higher Order Equations. Exercises 4.1, page 141
Problem number : 28
Date solved : Thursday, March 13, 2025 at 07:52:12 AM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} y^{\prime \prime }+10 y^{\prime }+25 y&=0 \end{align*}

Using reduction of order method given that one solution is

\begin{align*} y&={\mathrm e}^{-5 t} \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 14

ode:=diff(diff(y(t),t),t)+10*diff(y(t),t)+25*y(t) = 0; 
dsolve(ode,y(t), singsol=all);
 

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

✓ Mathematica. Time used: 0.014 (sec). Leaf size: 18

ode=D[y[t],{t,2}]+10*D[y[t],t]+25*y[t]==0; 
ic={}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\[ y(t)\to e^{-5 t} (c_2 t+c_1) \]

✓ Sympy. Time used: 0.148 (sec). Leaf size: 12

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(25*y(t) + 10*Derivative(y(t), t) + Derivative(y(t), (t, 2)),0) 
ics = {} 
dsolve(ode,func=y(t),ics=ics)
 

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