23.3.567 problem 575

Internal problem ID [6281]
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 : 575
Date solved : Tuesday, September 30, 2025 at 02:42:12 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

✓ Maple. Time used: 0.004 (sec). Leaf size: 36

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

\[ y = \frac {\left (7 c_1 +6 c_2 \right ) x^{3}+\left (-9 c_1 -6 c_2 \right ) x^{2}+3 c_1 x +c_2}{x^{2}} \]

✓ Mathematica. Time used: 0.041 (sec). Leaf size: 35

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

\begin{align*} y(x)&\to \frac {c_2 \left (12 x^2-18 x+7\right )-3 c_1 (x-1)^3}{3 x^2} \end{align*}

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x**2*(1 - 2*x)*(1 - x)*Derivative(y(x), (x, 2)) + x*(4 - 6*x)*Derivative(y(x), x) + (6*x + 2)*y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

False