90.17.7 problem 7

Internal problem ID [25269]
Book : Ordinary Differential Equations. By William Adkins and Mark G Davidson. Springer. NY. 2010. ISBN 978-1-4614-3617-1
Section : Chapter 4. Linear Constant Coefficient Differential Equations. Exercises at page 291
Problem number : 7
Date solved : Thursday, October 02, 2025 at 11:59:28 PM
CAS classification : [[_3rd_order, _missing_x]]

\begin{align*} y^{\prime \prime \prime }+2 y^{\prime \prime }+25 y^{\prime }+50 y&=0 \end{align*}

✓ Maple. Time used: 0.001 (sec). Leaf size: 23

ode:=diff(diff(diff(y(t),t),t),t)+2*diff(diff(y(t),t),t)+25*diff(y(t),t)+50*y(t) = 0; 
dsolve(ode,y(t), singsol=all);
 

\[ y = c_1 \,{\mathrm e}^{-2 t}+c_2 \sin \left (5 t \right )+c_3 \cos \left (5 t \right ) \]

✓ Mathematica. Time used: 0.002 (sec). Leaf size: 28

ode=D[y[t],{t,3}]+2*D[y[t],{t,2}]+25*D[y[t],{t,1}]+50*y[t]==0; 
ic={}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\begin{align*} y(t)&\to c_3 e^{-2 t}+c_1 \cos (5 t)+c_2 \sin (5 t) \end{align*}

✓ Sympy. Time used: 0.110 (sec). Leaf size: 22

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(50*y(t) + 25*Derivative(y(t), t) + 2*Derivative(y(t), (t, 2)) + Derivative(y(t), (t, 3)),0) 
ics = {} 
dsolve(ode,func=y(t),ics=ics)
 

\[ y{\left (t \right )} = C_{1} e^{- 2 t} + C_{2} \sin {\left (5 t \right )} + C_{3} \cos {\left (5 t \right )} \]