12.20.1 problem section 9.4, problem 3

Internal problem ID [2222]
Book : Elementary differential equations with boundary value problems. William F. Trench. Brooks/Cole 2001
Section : Chapter 9 Introduction to Linear Higher Order Equations. Section 9.4. Variation of Parameters for Higher Order Equations. Page 503
Problem number : section 9.4, problem 3
Date solved : Tuesday, March 04, 2025 at 01:51:59 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&=2 x \end{align*}

✓ Maple. Time used: 0.009 (sec). Leaf size: 26

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) = 2*x; 
dsolve(ode,y(x), singsol=all);
 

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

✓ Mathematica. Time used: 0.006 (sec). Leaf size: 25

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]==2*x; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

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

✓ Sympy. Time used: 0.272 (sec). Leaf size: 17

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

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