58.8.10 problem 13

Internal problem ID [14679]
Book : Differential Equations by Shepley L. Ross. Third edition. John Willey. New Delhi. 2004.
Section : Chapter 4, Section 4.1. Basic theory of linear differential equations. Exercises page 113
Problem number : 13
Date solved : Thursday, October 02, 2025 at 09:50:09 AM
CAS classification : [[_3rd_order, _with_linear_symmetries]]

\begin{align*} x^{3} y^{\prime \prime \prime }-4 x^{2} y^{\prime \prime }+8 x y^{\prime }-8 y&=0 \end{align*}

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

ode:=x^3*diff(diff(diff(y(x),x),x),x)-4*x^2*diff(diff(y(x),x),x)+8*x*diff(y(x),x)-8*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

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

✓ Mathematica. Time used: 0.003 (sec). Leaf size: 20

ode=x^3*D[y[x],{x,3}]-4*x^2*D[y[x],{x,2}]+8*x*D[y[x],x]-8*y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to x \left (c_3 x^3+c_2 x+c_1\right ) \end{align*}

✓ Sympy. Time used: 0.119 (sec). Leaf size: 14

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x**3*Derivative(y(x), (x, 3)) - 4*x**2*Derivative(y(x), (x, 2)) + 8*x*Derivative(y(x), x) - 8*y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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