76.38.2 problem Ex. 2

Internal problem ID [20217]
Book : Introductory Course On Differential Equations by Daniel A Murray. Longmans Green and Co. NY. 1924
Section : Chapter VII. Linear equations with variable coefficients. Problems at page 91
Problem number : Ex. 2
Date solved : Thursday, October 02, 2025 at 05:34:50 PM
CAS classification : [[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, `_with_symmetry_[0,F(x)]`]]

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

✓ Maple. Time used: 0.002 (sec). Leaf size: 22

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

\[ y = \left (2 x -1\right ) \left ({\mathrm e}^{\frac {1}{4 x -2}} c_1 +c_2 \right ) \]

✓ Mathematica. Time used: 0.059 (sec). Leaf size: 27

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

\begin{align*} y(x)&\to -\left ((2 x-1) \left (c_1 e^{\frac {1}{4 x-2}}+c_2\right )\right ) \end{align*}

✗ Sympy

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

False