3.2.24 problem problem 54

Internal problem ID [958]
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 54
Date solved : Tuesday, September 30, 2025 at 04:19:59 AM
CAS classification : [[_3rd_order, _missing_y]]

\begin{align*} x^{3} y^{\prime \prime \prime }+6 x^{2} y^{\prime \prime }+4 x y^{\prime }&=0 \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 15

ode:=x^3*diff(diff(diff(y(x),x),x),x)+6*x^2*diff(diff(y(x),x),x)+4*x*diff(y(x),x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = c_1 +c_2 \ln \left (x \right )+\frac {c_3}{x^{3}} \]

✓ Mathematica. Time used: 0.011 (sec). Leaf size: 22

ode=x^3*D[y[x],{x,3}]+6*x^2*D[y[x],{x,2}]+4*x*D[y[x],x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

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

✓ Sympy. Time used: 0.106 (sec). Leaf size: 14

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x**3*Derivative(y(x), (x, 3)) + 6*x**2*Derivative(y(x), (x, 2)) + 4*x*Derivative(y(x), x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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