6.20.6 problem section 9.4, problem 18

Internal problem ID [2227]
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 18
Date solved : Tuesday, September 30, 2025 at 05:25:13 AM
CAS classification : [[_high_order, _exact, _linear, _nonhomogeneous]]

\begin{align*} x^{4} y^{\prime \prime \prime \prime }+6 x^{3} y^{\prime \prime \prime }+2 x^{2} y^{\prime \prime }-4 x y^{\prime }+4 y&=12 x^{2} \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 39

ode:=x^4*diff(diff(diff(diff(y(x),x),x),x),x)+6*x^3*diff(diff(diff(y(x),x),x),x)+2*x^2*diff(diff(y(x),x),x)-4*x*diff(y(x),x)+4*y(x) = 12*x^2; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {12 \ln \left (x \right ) x^{4}+\left (12 c_2 -15\right ) x^{4}+12 c_3 \,x^{3}+2 c_1 x +12 c_4}{12 x^{2}} \]

✓ Mathematica. Time used: 0.004 (sec). Leaf size: 38

ode=x^4*D[y[x],{x,4}]+6*x^3*D[y[x],{x,3}]+2*x^2*D[y[x],{x,2}]-4*x*D[y[x],x]+4*y[x]==12*x^2; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \frac {x^4 \log (x)+\left (-\frac {19}{12}+c_4\right ) x^4+c_3 x^3+c_2 x+c_1}{x^2} \end{align*}

✓ Sympy. Time used: 0.229 (sec). Leaf size: 24

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x**4*Derivative(y(x), (x, 4)) + 6*x**3*Derivative(y(x), (x, 3)) + 2*x**2*Derivative(y(x), (x, 2)) - 12*x**2 - 4*x*Derivative(y(x), x) + 4*y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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