12.20.5 problem section 9.4, problem 16

Internal problem ID [2226]
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 16
Date solved : Tuesday, March 04, 2025 at 01:52:03 PM
CAS classification : [[_high_order, _with_linear_symmetries]]

\begin{align*} x^{4} y^{\prime \prime \prime \prime }-4 x^{3} y^{\prime \prime \prime }+12 x^{2} y^{\prime \prime }-24 x y^{\prime }+24 y&=x^{4} \end{align*}

✓ Maple. Time used: 0.012 (sec). Leaf size: 30

ode:=x^4*diff(diff(diff(diff(y(x),x),x),x),x)-4*x^3*diff(diff(diff(y(x),x),x),x)+12*x^2*diff(diff(y(x),x),x)-24*x*diff(y(x),x)+24*y(x) = x^4; 
dsolve(ode,y(x), singsol=all);
 

\[ y = x \left (\frac {x^{3} \ln \left (x \right )}{6}+\left (c_4 -\frac {11}{36}\right ) x^{3}+c_3 \,x^{2}+c_2 x +c_1 \right ) \]

✓ Mathematica. Time used: 0.007 (sec). Leaf size: 40

ode=x^4*D[y[x],{x,4}]-4*x^3*D[y[x],{x,3}]+12*x^2*D[y[x],{x,2}]-24*x*D[y[x],x]+24*y[x]==x^4; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to \frac {1}{6} x^4 \log (x)+x \left (\left (-\frac {11}{36}+c_4\right ) x^3+c_3 x^2+c_2 x+c_1\right ) \]

✓ Sympy. Time used: 0.409 (sec). Leaf size: 27

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x**4*Derivative(y(x), (x, 4)) - x**4 - 4*x**3*Derivative(y(x), (x, 3)) + 12*x**2*Derivative(y(x), (x, 2)) - 24*x*Derivative(y(x), x) + 24*y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = x \left (C_{1} + C_{2} x + C_{3} x^{2} + C_{4} x^{3} + \frac {x^{3} \log {\left (x \right )}}{6}\right ) \]