76.39.5 problem Ex. 5

Internal problem ID [20222]
Book : Introductory Course On Differential Equations by Daniel A Murray. Longmans Green and Co. NY. 1924
Section : Chapter VII. Linear equations with variable coefficients. End of chapter problems at page 91
Problem number : Ex. 5
Date solved : Thursday, October 02, 2025 at 05:34:54 PM
CAS classification : [[_3rd_order, _with_linear_symmetries]]

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

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

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)-4*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

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

✓ Mathematica. Time used: 0.003 (sec). Leaf size: 23

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

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

✓ Sympy. Time used: 0.126 (sec). Leaf size: 19

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) - 4*y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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