68.15.63 problem 64 (c)

Internal problem ID [17789]
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 (c)
Date solved : Thursday, October 02, 2025 at 02:28:16 PM
CAS classification : [[_high_order, _exact, _linear, _homogeneous]]

\begin{align*} x^{4} y^{\prime \prime \prime \prime }+14 x^{3} y^{\prime \prime \prime }+55 x^{2} y^{\prime \prime }+65 x y^{\prime }+15 y&=0 \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 27

ode:=x^4*diff(diff(diff(diff(y(x),x),x),x),x)+14*x^3*diff(diff(diff(y(x),x),x),x)+55*x^2*diff(diff(y(x),x),x)+65*x*diff(y(x),x)+15*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {c_3 \sin \left (\ln \left (x \right )\right ) x +c_4 \cos \left (\ln \left (x \right )\right ) x +c_2 \,x^{2}+c_1}{x^{3}} \]

✓ Mathematica. Time used: 0.004 (sec). Leaf size: 32

ode=x^4*D[y[x],{x,4}]+14*x^3*D[y[x],{x,3}]+55*x^2*D[y[x],{x,2}]+65*x*D[y[x],x]+15*y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \frac {c_4 x^2+c_2 x \cos (\log (x))+c_1 x \sin (\log (x))+c_3}{x^3} \end{align*}

✓ Sympy. Time used: 0.188 (sec). Leaf size: 26

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x**4*Derivative(y(x), (x, 4)) + 14*x**3*Derivative(y(x), (x, 3)) + 55*x**2*Derivative(y(x), (x, 2)) + 65*x*Derivative(y(x), x) + 15*y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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