23.3.227 problem 229

Internal problem ID [5941]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Part II. Chapter 3. THE DIFFERENTIAL EQUATION IS LINEAR AND OF SECOND ORDER, page 311
Problem number : 229
Date solved : Tuesday, September 30, 2025 at 02:06:32 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} 3 \left (2-x \right ) y-\left (9-4 x \right ) y^{\prime }+\left (3-x \right ) y^{\prime \prime }&=0 \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 30

ode:=3*(2-x)*y(x)-(9-4*x)*diff(y(x),x)+(-x+3)*diff(diff(y(x),x),x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = {\mathrm e}^{x} \left (c_1 +c_2 \left (4 x^{3}-42 x^{2}+150 x -183\right ) {\mathrm e}^{2 x}\right ) \]

✓ Mathematica. Time used: 0.13 (sec). Leaf size: 42

ode=3*(2 - x)*y[x] - (9 - 4*x)*D[y[x],x] + (3 - x)*D[y[x],{x,2}] == 0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \frac {1}{8} c_2 e^{3 x-9} \left (4 x^3-42 x^2+150 x-183\right )+c_1 e^{x-3} \end{align*}

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq((3 - x)*Derivative(y(x), (x, 2)) + (6 - 3*x)*y(x) - (9 - 4*x)*Derivative(y(x), x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

False