23.5.178 problem 178

Internal problem ID [6787]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Part II. Chapter 5. THE EQUATION IS LINEAR AND OF ORDER GREATER THAN TWO, page 410
Problem number : 178
Date solved : Tuesday, September 30, 2025 at 03:51:41 PM
CAS classification : [[_high_order, _missing_y]]

\begin{align*} 12 x^{2} y^{\prime \prime }+8 x^{3} y^{\prime \prime \prime }+x^{4} y^{\prime \prime \prime \prime }&=0 \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 19

ode:=12*x^2*diff(diff(y(x),x),x)+8*x^3*diff(diff(diff(y(x),x),x),x)+x^4*diff(diff(diff(diff(y(x),x),x),x),x) = 0; 
dsolve(ode,y(x), singsol=all);
 

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

✓ Mathematica. Time used: 0.012 (sec). Leaf size: 27

ode=12*x^2*D[y[x],{x,2}] + 8*x^3*D[y[x],{x,3}] + x^4*D[y[x],{x,4}] == 0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \frac {3 c_2 x+c_1}{6 x^2}+c_4 x+c_3 \end{align*}

✓ Sympy. Time used: 0.073 (sec). Leaf size: 15

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x**4*Derivative(y(x), (x, 4)) + 8*x**3*Derivative(y(x), (x, 3)) + 12*x**2*Derivative(y(x), (x, 2)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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