73.16.18 problem 24.3 (b)

Internal problem ID [15459]
Book : Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell. second edition. CRC Press. FL, USA. 2020
Section : Chapter 24. Variation of parameters. Additional exercises page 444
Problem number : 24.3 (b)
Date solved : Monday, March 31, 2025 at 01:38:30 PM
CAS classification : [[_3rd_order, _with_linear_symmetries]]

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

✓ Maple. Time used: 0.007 (sec). Leaf size: 30

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

\[ y = \frac {\ln \left (x \right ) x^{3}}{2}+\frac {\left (4 c_3 -3\right ) x^{3}}{4}+c_2 \,x^{2}+c_1 x \]

✓ Mathematica. Time used: 0.006 (sec). Leaf size: 34

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

\[ y(x)\to \frac {1}{2} x^3 \log (x)+x \left (\left (-\frac {3}{4}+c_3\right ) x^2+c_2 x+c_1\right ) \]

✓ Sympy. Time used: 0.307 (sec). Leaf size: 22

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

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