68.15.62 problem 64 (b)

Internal problem ID [17788]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 4. Higher Order Equations. Exercises 4.7, page 195
Problem number : 64 (b)
Date solved : Thursday, October 02, 2025 at 02:28:16 PM
CAS classification : [[_high_order, _with_linear_symmetries]]

\begin{align*} x^{4} y^{\prime \prime \prime \prime }+5 x^{3} y^{\prime \prime \prime }-12 x^{2} y^{\prime \prime }-12 x y^{\prime }+48 y&=0 \end{align*}

✓ Maple. Time used: 0.005 (sec). Leaf size: 23

ode:=x^4*diff(diff(diff(diff(y(x),x),x),x),x)+5*x^3*diff(diff(diff(y(x),x),x),x)-12*x^2*diff(diff(y(x),x),x)-12*x*diff(y(x),x)+48*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {c_3 \,x^{7}+c_1 \,x^{5}+c_4 x +c_2}{x^{3}} \]

✓ Mathematica. Time used: 0.004 (sec). Leaf size: 28

ode=x^4*D[y[x],{x,4}]+5*x^3*D[y[x],{x,3}]-12*x^2*D[y[x],{x,2}]-12*x*D[y[x],x]+48*y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \frac {c_4 x^7+c_3 x^5+c_2 x+c_1}{x^3} \end{align*}

✓ Sympy. Time used: 0.146 (sec). Leaf size: 22

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x**4*Derivative(y(x), (x, 4)) + 5*x**3*Derivative(y(x), (x, 3)) - 12*x**2*Derivative(y(x), (x, 2)) - 12*x*Derivative(y(x), x) + 48*y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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