3.2.10 problem problem 19

Internal problem ID [944]
Book : Differential equations and linear algebra, 4th ed., Edwards and Penney
Section : Section 5.3, Higher-Order Linear Differential Equations. Homogeneous Equations with Constant Coefficients. Page 300
Problem number : problem 19
Date solved : Tuesday, September 30, 2025 at 04:19:53 AM
CAS classification : [[_3rd_order, _missing_x]]

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

✓ Maple. Time used: 0.002 (sec). Leaf size: 19

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

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

✓ Mathematica. Time used: 0.002 (sec). Leaf size: 26

ode=D[y[x],{x,3}]+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_2 x+c_3 e^{2 x}+c_1\right ) \end{align*}

✓ Sympy. Time used: 0.091 (sec). Leaf size: 15

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

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