37.3.8 problem 10.4.8 (h)

Internal problem ID [6414]
Book : Basic Training in Mathematics. By R. Shankar. Plenum Press. NY. 1995
Section : Chapter 10, Differential equations. Section 10.4, ODEs with variable Coefficients. Second order and Homogeneous. page 318
Problem number : 10.4.8 (h)
Date solved : Sunday, March 30, 2025 at 10:55:02 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

✓ Maple. Time used: 0.004 (sec). Leaf size: 27

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

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

✓ Mathematica. Time used: 0.035 (sec). Leaf size: 33

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

\[ y(x)\to \frac {-c_2 x^2-c_1 x+2 c_2 x \log (x)+c_2}{x-1} \]

✗ Sympy

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

NotImplementedError : The given ODE x*(x - 1)**2*Derivative(y(x), (x, 2)) - 2*y(x) cannot be solved by the hypergeometric method