23.3.563 problem 571

Internal problem ID [6277]
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 : 571
Date solved : Tuesday, September 30, 2025 at 02:42:07 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

✓ Maple. Time used: 0.006 (sec). Leaf size: 67

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

\[ y = \sqrt {\left (a -x \right ) x}\, \left (\left (\frac {x}{a -x}\right )^{\frac {\sqrt {a^{2}-4 b}}{2 a}} c_2 +\left (\frac {a -x}{x}\right )^{\frac {\sqrt {a^{2}-4 b}}{2 a}} c_1 \right ) \]

✓ Mathematica. Time used: 17.684 (sec). Leaf size: 121

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

\begin{align*} y(x)&\to \frac {x^{\frac {1}{2}-\frac {1}{2} \sqrt {1-\frac {4 b}{a^2}}} (x-a)^{\frac {1}{2}-\frac {1}{2} \sqrt {1-\frac {4 b}{a^2}}} \left (a c_1 \sqrt {1-\frac {4 b}{a^2}} x^{\sqrt {1-\frac {4 b}{a^2}}}+c_2 (x-a)^{\sqrt {1-\frac {4 b}{a^2}}}\right )}{a \sqrt {1-\frac {4 b}{a^2}}} \end{align*}

✗ Sympy

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

NotImplementedError : The given ODE b*y(x) + x**2*(a - x)**2*Derivative(y(x), (x, 2)) cannot be solv