74.13.6 problem 23

Internal problem ID [16293]
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 : 23
Date solved : Thursday, March 13, 2025 at 08:10:05 AM
CAS classification : [[_3rd_order, _missing_x]]

\begin{align*} 3 y^{\prime \prime \prime }-4 y^{\prime \prime }-5 y^{\prime }+2 y&=0 \end{align*}

✓ Maple. Time used: 0.005 (sec). Leaf size: 23

ode:=3*diff(diff(diff(y(t),t),t),t)-4*diff(diff(y(t),t),t)-5*diff(y(t),t)+2*y(t) = 0; 
dsolve(ode,y(t), singsol=all);
 

\[ y = \left (c_{3} {\mathrm e}^{3 t}+c_{1} {\mathrm e}^{\frac {4 t}{3}}+c_{2} \right ) {\mathrm e}^{-t} \]

✓ Mathematica. Time used: 0.004 (sec). Leaf size: 32

ode=3*D[ y[t],{t,3}]-4*D[y[t],{t,2}]-5*D[y[t],t]+2*y[t]==0; 
ic={}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\[ y(t)\to e^{-t} \left (c_1 e^{4 t/3}+c_3 e^{3 t}+c_2\right ) \]

✓ Sympy. Time used: 0.174 (sec). Leaf size: 20

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(2*y(t) - 5*Derivative(y(t), t) - 4*Derivative(y(t), (t, 2)) + 3*Derivative(y(t), (t, 3)),0) 
ics = {} 
dsolve(ode,func=y(t),ics=ics)
 

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