9.2.4 problem problem 13

Internal problem ID [938]
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 13
Date solved : Tuesday, March 04, 2025 at 12:06:12 PM
CAS classification : [[_3rd_order, _missing_x]]

\begin{align*} 9 y^{\prime \prime \prime }+12 y^{\prime \prime }+4 y^{\prime }&=0 \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 16

ode:=9*diff(diff(diff(y(x),x),x),x)+12*diff(diff(y(x),x),x)+4*diff(y(x),x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \left (x c_3 +c_2 \right ) {\mathrm e}^{-\frac {2 x}{3}}+c_1 \]

✓ Mathematica. Time used: 0.026 (sec). Leaf size: 32

ode=9*D[y[x],{x,3}]+12*D[y[x],{x,2}]+4*D[y[x],x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to c_3-\frac {3}{4} e^{-2 x/3} (c_2 (2 x+3)+2 c_1) \]

✓ Sympy. Time used: 0.179 (sec). Leaf size: 15

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(4*Derivative(y(x), x) + 12*Derivative(y(x), (x, 2)) + 9*Derivative(y(x), (x, 3)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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