23.5.112 problem 112

Internal problem ID [6721]
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 : 112
Date solved : Tuesday, September 30, 2025 at 03:51:08 PM
CAS classification : [[_3rd_order, _fully, _exact, _linear]]

\begin{align*} -4 y-14 x y^{\prime }+\left (-8 x^{2}+3\right ) y^{\prime \prime }+x \left (-x^{2}+1\right ) y^{\prime \prime \prime }&=0 \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 41

ode:=-4*y(x)-14*x*diff(y(x),x)+(-8*x^2+3)*diff(diff(y(x),x),x)+x*(-x^2+1)*diff(diff(diff(y(x),x),x),x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {\frac {c_3}{\sqrt {x -1}\, \sqrt {x +1}}+c_1 +\frac {c_2 \ln \left (x +\sqrt {x^{2}-1}\right )}{\sqrt {x^{2}-1}}}{x} \]

✓ Mathematica. Time used: 0.038 (sec). Leaf size: 50

ode=-4*y[x] - 14*x*D[y[x],x] + (3 - 8*x^2)*D[y[x],{x,2}] + x*(1 - x^2)*D[y[x],{x,3}] == 0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \frac {-\frac {c_3 \text {arctanh}\left (\frac {x}{\sqrt {x^2-1}}\right )}{\sqrt {x^2-1}}-\frac {c_2}{\sqrt {x^2-1}}+c_1}{x} \end{align*}

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x*(1 - x**2)*Derivative(y(x), (x, 3)) - 14*x*Derivative(y(x), x) + (3 - 8*x**2)*Derivative(y(x), (x, 2)) - 4*y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

NotImplementedError : The given ODE Derivative(y(x), x) - (x*(-x**2*Derivative(y(x), (x, 3)) - 8*x*D