23.5.115 problem 115

Internal problem ID [6724]
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 : 115
Date solved : Tuesday, September 30, 2025 at 03:51:09 PM
CAS classification : [NONE]

\begin{align*} -6 y+6 \left (1+x \right ) y^{\prime }-3 x \left (2+x \right ) y^{\prime \prime }+x^{2} \left (3+y\right ) y^{\prime \prime \prime }&=0 \end{align*}

✗ Maple

ode:=-6*y(x)+6*(1+x)*diff(y(x),x)-3*x*(x+2)*diff(diff(y(x),x),x)+x^2*(3+y(x))*diff(diff(diff(y(x),x),x),x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ \text {No solution found} \]

✗ Mathematica

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

Not solved

✗ Sympy

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

NotImplementedError : The given ODE Derivative(y(x), x) - (-x**2*y(x)*Derivative(y(x), (x, 3))/6 + x