74.13.2 problem 19

Internal problem ID [16289]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 4. Higher Order Equations. Exercises 4.5, page 175
Problem number : 19
Date solved : Thursday, March 13, 2025 at 08:10:03 AM
CAS classification : [[_3rd_order, _missing_x]]

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

✓ Maple. Time used: 0.003 (sec). Leaf size: 16

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

\[ y = \left (c_{3} t +c_{2} \right ) {\mathrm e}^{5 t}+c_{1} \]

✓ Mathematica. Time used: 3.946 (sec). Leaf size: 89

ode=D[ y[t],{t,3}]-10*D[y[t],{t,2}]+25*D[y[t],t]==0; 
ic={}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\begin{align*} y(t)\to \int _1^te^{5 K[1]} (c_1+c_2 K[1])dK[1]+c_3 \\ y(t)\to \frac {1}{5} c_1 e^{5 t}-\frac {e^5 c_1}{5}+c_3 \\ y(t)\to \frac {1}{25} c_2 e^{5 t} (5 t-1)-\frac {4 e^5 c_2}{25}+c_3 \\ \end{align*}

✓ Sympy. Time used: 0.146 (sec). Leaf size: 14

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(25*Derivative(y(t), t) - 10*Derivative(y(t), (t, 2)) + Derivative(y(t), (t, 3)),0) 
ics = {} 
dsolve(ode,func=y(t),ics=ics)
 

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