23.5.117 problem 117

Internal problem ID [6726]
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 : 117
Date solved : Friday, October 03, 2025 at 02:09:50 AM
CAS classification : [[_3rd_order, _with_linear_symmetries]]

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

✓ Maple. Time used: 0.001 (sec). Leaf size: 37

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

\[ y = c_1 x -\frac {c_1}{2}+c_2 \left (x -\frac {1}{2}\right )^{1+\frac {\sqrt {3}}{2}}+c_3 \left (x -\frac {1}{2}\right )^{1-\frac {\sqrt {3}}{2}} \]

✓ Mathematica. Time used: 0.003 (sec). Leaf size: 50

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

\begin{align*} y(x)&\to (2 x-1) \left (c_2 (2 x-1)^{\frac {\sqrt {3}}{2}}+c_1 (2 x-1)^{-\frac {\sqrt {3}}{2}}+c_3\right ) \end{align*}

✗ Sympy

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

NotImplementedError : The given ODE Derivative(y(x), x) - (-8*x**3*Derivative(y(x), (x, 3)) + 12*x**