23.3.565 problem 573

Internal problem ID [6279]
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 : 573
Date solved : Tuesday, September 30, 2025 at 02:42:09 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

✓ Maple. Time used: 0.015 (sec). Leaf size: 143

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

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

✓ Mathematica. Time used: 2.086 (sec). Leaf size: 152

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

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

✗ Sympy

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

False