23.3.468 problem 474

Internal problem ID [6182]
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 : 474
Date solved : Tuesday, September 30, 2025 at 02:24:15 PM
CAS classification : [[_2nd_order, _exact, _linear, _homogeneous]]

\begin{align*} -9 y-3 \left (1-3 x \right ) y^{\prime }+\left (1-3 x \right )^{2} y^{\prime \prime }&=0 \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 24

ode:=-9*y(x)-3*(1-3*x)*diff(y(x),x)+(1-3*x)^2*diff(diff(y(x),x),x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {9 \left (-\frac {1}{3}+x \right )^{2} c_1 +9 c_2}{9 x -3} \]

✓ Mathematica. Time used: 0.019 (sec). Leaf size: 39

ode=-9*y[x] - 3*(1 - 3*x)*D[y[x],x] + (1 - 3*x)^2*D[y[x],{x,2}] == 0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \frac {c_1 \left (-9 x^2+6 x-2\right )-3 i c_2 x (3 x-2)}{6 x-2} \end{align*}

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq((1 - 3*x)**2*Derivative(y(x), (x, 2)) - (3 - 9*x)*Derivative(y(x), x) - 9*y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

False