5.2.10 problem 17

Internal problem ID [1481]
Book : Elementary differential equations and boundary value problems, 11th ed., Boyce, DiPrima, Meade
Section : Chapter 4.2, Higher order linear differential equations. Constant coefficients. page 180
Problem number : 17
Date solved : Tuesday, September 30, 2025 at 04:34:31 AM
CAS classification : [[_3rd_order, _missing_x]]

\begin{align*} y^{\prime \prime \prime }+5 y^{\prime \prime }+6 y^{\prime }+2 y&=0 \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 32

ode:=diff(diff(diff(y(x),x),x),x)+5*diff(diff(y(x),x),x)+6*diff(y(x),x)+2*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = c_1 \,{\mathrm e}^{-x}+c_2 \,{\mathrm e}^{\left (-2+\sqrt {2}\right ) x}+c_3 \,{\mathrm e}^{-\left (2+\sqrt {2}\right ) x} \]

✓ Mathematica. Time used: 0.002 (sec). Leaf size: 43

ode=D[y[x],{x,3}]+5*D[y[x],{x,2}]+6*D[y[x],x]+2*y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to e^{-x} \left (c_1 e^{-\left (\left (1+\sqrt {2}\right ) x\right )}+c_2 e^{\left (\sqrt {2}-1\right ) x}+c_3\right ) \end{align*}

✓ Sympy. Time used: 0.154 (sec). Leaf size: 31

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(2*y(x) + 6*Derivative(y(x), x) + 5*Derivative(y(x), (x, 2)) + Derivative(y(x), (x, 3)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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