12.20.4 problem section 9.4, problem 14

Internal problem ID [2225]
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 14
Date solved : Tuesday, March 04, 2025 at 01:52:02 PM
CAS classification : [[_high_order, _with_linear_symmetries]]

\begin{align*} 16 x^{4} y^{\prime \prime \prime \prime }+96 x^{3} y^{\prime \prime \prime }+72 x^{2} y^{\prime \prime }-24 x y^{\prime }+9 y&=96 x^{{5}/{2}} \end{align*}

✓ Maple. Time used: 0.011 (sec). Leaf size: 32

ode:=16*x^4*diff(diff(diff(diff(y(x),x),x),x),x)+96*x^3*diff(diff(diff(y(x),x),x),x)+72*x^2*diff(diff(y(x),x),x)-24*x*diff(y(x),x)+9*y(x) = 96*x^(5/2); 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {4 c_4 \,x^{3}+x^{4}+4 c_3 \,x^{2}+4 c_2 x +4 c_1}{4 x^{{3}/{2}}} \]

✓ Mathematica. Time used: 0.009 (sec). Leaf size: 41

ode=16*x^4*D[y[x],{x,4}]+96*x^3*D[y[x],{x,3}]+72*x^2*D[y[x],{x,2}]-24*x*D[y[x],x]+9*y[x]==96*x^(5/2); 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to \frac {x^4+4 c_4 x^3+4 c_3 x^2+4 c_2 x+4 c_1}{4 x^{3/2}} \]

✓ Sympy. Time used: 0.583 (sec). Leaf size: 26

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-96*x**(5/2) + 16*x**4*Derivative(y(x), (x, 4)) + 96*x**3*Derivative(y(x), (x, 3)) + 72*x**2*Derivative(y(x), (x, 2)) - 24*x*Derivative(y(x), x) + 9*y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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