77.41.14 problem 5 (i)

Internal problem ID [20778]
Book : A Text book for differentional equations for postgraduate students by Ray and Chaturvedi. First edition, 1958. BHASKAR press. INDIA
Section : Chapter VIII. Linear equations of second order. Excercise at end of chapter VIII. Page 141
Problem number : 5 (i)
Date solved : Thursday, October 02, 2025 at 06:23:09 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} \left (x^{3}-2 x^{2}\right ) y^{\prime \prime }+2 x^{2} y^{\prime }-12 \left (x -2\right ) y&=0 \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 20

ode:=(x^3-2*x^2)*diff(diff(y(x),x),x)+2*x^2*diff(y(x),x)-12*(x-2)*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {c_2 \,x^{7}+c_1}{x^{3} \left (x -2\right )} \]

✓ Mathematica. Time used: 0.026 (sec). Leaf size: 28

ode=(x^3-2*x^2)*D[y[x],{x,2}]+2*x^2*D[y[x],x]-12*(x-2)*y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \frac {c_2 x^7+7 c_1}{7 (x-2) x^3} \end{align*}

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(2*x**2*Derivative(y(x), x) - (12*x - 24)*y(x) + (x**3 - 2*x**2)*Derivative(y(x), (x, 2)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

False