23.3.475 problem 481

Internal problem ID [6189]
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 : 481
Date solved : Tuesday, September 30, 2025 at 02:36:00 PM
CAS classification : [[_2nd_order, _exact, _linear, _homogeneous]]

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

✓ Maple. Time used: 0.002 (sec). Leaf size: 19

ode:=-2*b*y(x)+2*a*diff(y(x),x)+x*(b*x+a)*diff(diff(y(x),x),x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {c_1 +c_2 \left (b x +a \right )^{3}}{x} \]

✓ Mathematica. Time used: 0.026 (sec). Leaf size: 30

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

\begin{align*} y(x)&\to \frac {\frac {c_2 (a+b x)^3}{b}+3 c_1}{3 x} \end{align*}

✗ Sympy

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

False