83.47.9 problem Ex 9 page 89

Internal problem ID [19515]
Book : A Text book for differentional equations for postgraduate students by Ray and Chaturvedi. First edition, 1958. BHASKAR press. INDIA
Section : Book Solved Excercises. Chapter VI. Homogeneous linear equations with variable coefficients
Problem number : Ex 9 page 89
Date solved : Monday, March 31, 2025 at 07:28:53 PM
CAS classification : [[_3rd_order, _with_linear_symmetries]]

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

✓ Maple. Time used: 0.002 (sec). Leaf size: 37

ode:=(2*x-1)^3*diff(diff(diff(y(x),x),x),x)+(2*x-1)*diff(y(x),x)-2*y(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: 0.005 (sec). Leaf size: 50

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

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

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq((2*x - 1)**3*Derivative(y(x), (x, 3)) + (2*x - 1)*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**2*Derivative(y(x), (x, 3)) - 6*x*Derivative(y(x), (x, 3)) + 2*y(x) + Derivative(y(x), (x, 3)))/(2*x - 1) cannot be solved by the factorable group method