90.13.11 problem 11

Internal problem ID [25223]
Book : Ordinary Differential Equations. By William Adkins and Mark G Davidson. Springer. NY. 2010. ISBN 978-1-4614-3617-1
Section : Chapter 3. Second Order Constant Coefficient Linear Differential Equations. Exercises at page 235
Problem number : 11
Date solved : Thursday, October 02, 2025 at 11:59:05 PM
CAS classification : [[_2nd_order, _missing_x]]

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

✓ Maple. Time used: 0.001 (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: 0.009 (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]
 

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

✓ Sympy. Time used: 0.084 (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)
 

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