23.5.179 problem 179

Internal problem ID [6788]
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 : 179
Date solved : Tuesday, September 30, 2025 at 03:51:41 PM
CAS classification : [[_high_order, _with_linear_symmetries]]

\begin{align*} a y+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: 0.004 (sec). Leaf size: 85

ode:=a*y(x)+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);
 

\[ y = \frac {c_1 \,x^{-\frac {\sqrt {5-4 \sqrt {-a +1}}}{2}}+c_2 \,x^{\frac {\sqrt {5-4 \sqrt {-a +1}}}{2}}+c_3 \,x^{-\frac {\sqrt {5+4 \sqrt {-a +1}}}{2}}+c_4 \,x^{\frac {\sqrt {5+4 \sqrt {-a +1}}}{2}}}{\sqrt {x}} \]

✓ Mathematica. Time used: 0.004 (sec). Leaf size: 116

ode=a*y[x] + 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 {c_1 x^{-\frac {1}{2} \sqrt {5-4 \sqrt {1-a}}}+c_2 x^{\frac {1}{2} \sqrt {5-4 \sqrt {1-a}}}+c_3 x^{-\frac {1}{2} \sqrt {4 \sqrt {1-a}+5}}+c_4 x^{\frac {1}{2} \sqrt {4 \sqrt {1-a}+5}}}{\sqrt {x}} \end{align*}

✗ Sympy

from sympy import * 
x = symbols("x") 
a = symbols("a") 
y = Function("y") 
ode = Eq(a*y(x) + 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)
 

NotImplementedError : CRootOf is not supported over ZZ[a]