43.7.3 problem 4(c)

Internal problem ID [8928]
Book : An introduction to Ordinary Differential Equations. Earl A. Coddington. Dover. NY 1961
Section : Chapter 2. Linear equations with constant coefficients. Page 74
Problem number : 4(c)
Date solved : Tuesday, September 30, 2025 at 06:00:15 PM
CAS classification : [[_3rd_order, _missing_x]]

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

✓ Maple. Time used: 0.003 (sec). Leaf size: 18

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

\[ y = c_1 +c_2 \,{\mathrm e}^{3 x}+c_3 \,{\mathrm e}^{2 x} \]

✓ Mathematica. Time used: 0.022 (sec). Leaf size: 30

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

\begin{align*} y(x)&\to \frac {1}{2} c_1 e^{2 x}+\frac {1}{3} c_2 e^{3 x}+c_3 \end{align*}

✓ Sympy. Time used: 0.087 (sec). Leaf size: 17

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(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)
 

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