26.7.14 problem Exercise 20.15, page 220

Internal problem ID [7064]
Book : Ordinary Differential Equations, By Tenenbaum and Pollard. Dover, NY 1963
Section : Chapter 4. Higher order linear differential equations. Lesson 20. Constant coefficients
Problem number : Exercise 20.15, page 220
Date solved : Tuesday, September 30, 2025 at 04:21:04 PM
CAS classification : [[_3rd_order, _missing_x]]

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

✓ Maple. Time used: 0.002 (sec). Leaf size: 20

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

\[ y = \left (c_1 \,{\mathrm e}^{\frac {4 x}{3}}+c_3 x +c_2 \right ) {\mathrm e}^{-x} \]

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

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

\begin{align*} y(x)&\to e^{-x} \left (c_1 e^{4 x/3}+c_3 x+c_2\right ) \end{align*}

✓ Sympy. Time used: 0.082 (sec). Leaf size: 17

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

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