83.34.1 problem 1

Internal problem ID [19343]
Book : A Text book for differentional equations for postgraduate students by Ray and Chaturvedi. First edition, 1958. BHASKAR press. INDIA
Section : Chapter VII. Exact differential equations and certain particular forms of equations. Exercise VII (H) at page 118
Problem number : 1
Date solved : Monday, March 31, 2025 at 07:09:05 PM
CAS classification : [[_3rd_order, _with_linear_symmetries]]

\begin{align*} n \,x^{3} y^{\prime \prime \prime }&=y-x y^{\prime } \end{align*}

✓ Maple. Time used: 0.004 (sec). Leaf size: 44

ode:=n*x^3*diff(diff(diff(y(x),x),x),x) = y(x)-x*diff(y(x),x); 
dsolve(ode,y(x), singsol=all);
 

\[ y = c_1 x +c_2 \,x^{\frac {n +\sqrt {n \left (-1+n \right )}}{n}}+c_3 \,x^{\frac {n -\sqrt {n \left (-1+n \right )}}{n}} \]

✓ Mathematica. Time used: 0.004 (sec). Leaf size: 47

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

\[ y(x)\to x \left (c_1 x^{-\frac {\sqrt {(n-1) n}}{n}}+c_2 x^{\frac {\sqrt {(n-1) n}}{n}}+c_3\right ) \]

✗ Sympy

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

NotImplementedError : The given ODE Derivative(y(x), x) - (-n*x**3*Derivative(y(x), (x, 3)) + y(x))/x cannot be solved by the factorable group method