23.5.85 problem 85

Internal problem ID [6694]
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 : 85
Date solved : Tuesday, September 30, 2025 at 03:50:54 PM
CAS classification : [[_3rd_order, _missing_y]]

\begin{align*} 6 n y^{\prime }-2 \left (n +1\right ) x y^{\prime \prime }+x^{2} y^{\prime \prime \prime }&=0 \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 20

ode:=6*n*diff(y(x),x)-2*(n+1)*x*diff(diff(y(x),x),x)+x^2*diff(diff(diff(y(x),x),x),x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = c_1 +c_2 \,x^{4}+c_3 \,x^{2 n +1} \]

✓ Mathematica. Time used: 0.03 (sec). Leaf size: 34

ode=6*n*D[y[x],x] - 2*(1 + n)*x*D[y[x],{x,2}] + x^2*D[y[x],{x,3}] == 0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \frac {c_1 x^{2 n+1}}{2 n+1}+\frac {c_2 x^4}{4}+c_3 \end{align*}

✗ Sympy

from sympy import * 
x = symbols("x") 
n = symbols("n") 
y = Function("y") 
ode = Eq(6*n*Derivative(y(x), x) + x**2*Derivative(y(x), (x, 3)) - x*(2*n + 2)*Derivative(y(x), (x, 2)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

NotImplementedError : The given ODE Derivative(y(x), x) - x*(2*n*Derivative(y(x), (x, 2)) - x*Deriva