78.15.23 problem 23

Internal problem ID [18308]
Book : DIFFERENTIAL EQUATIONS WITH APPLICATIONS AND HISTORICAL NOTES by George F. Simmons. 3rd edition. 2017. CRC press, Boca Raton FL.
Section : Chapter 3. Second order linear equations. Section 22. Higher Order Linear Equations. Coupled Harmonic Oscillators. Problems at page 160
Problem number : 23
Date solved : Monday, March 31, 2025 at 05:25:15 PM
CAS classification : [[_high_order, _missing_y]]

\begin{align*} x^{3} y^{\prime \prime \prime \prime }+8 x^{2} y^{\prime \prime \prime }+8 x y^{\prime \prime }-8 y^{\prime }&=0 \end{align*}

✓ Maple. Time used: 0.004 (sec). Leaf size: 21

ode:=x^3*diff(diff(diff(diff(y(x),x),x),x),x)+8*x^2*diff(diff(diff(y(x),x),x),x)+8*x*diff(diff(y(x),x),x)-8*diff(y(x),x) = 0; 
dsolve(ode,y(x), singsol=all);
 

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

✓ Mathematica. Time used: 0.006 (sec). Leaf size: 33

ode=x^3*D[y[x],{x,4}]+8*x^2*D[y[x],{x,3}]+8*x*D[y[x],{x,2}]-8*D[y[x],x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

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

✓ Sympy. Time used: 0.218 (sec). Leaf size: 17

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x**3*Derivative(y(x), (x, 4)) + 8*x**2*Derivative(y(x), (x, 3)) + 8*x*Derivative(y(x), (x, 2)) - 8*Derivative(y(x), x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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