23.3.520 problem 526

Internal problem ID [6234]
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 : 526
Date solved : Tuesday, September 30, 2025 at 02:37:33 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} -\left (1+x \right ) y+\left (3-5 x \right ) x y^{\prime }+2 \left (1-x \right ) x^{2} y^{\prime \prime }&=0 \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 33

ode:=-(1+x)*y(x)+(3-5*x)*x*diff(y(x),x)+2*(1-x)*x^2*diff(diff(y(x),x),x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {c_2 \ln \left (-1+\sqrt {x}\right )-c_2 \ln \left (1+\sqrt {x}\right )+2 c_2 \sqrt {x}+c_1}{x} \]

✓ Mathematica. Time used: 0.038 (sec). Leaf size: 31

ode=-((1 + x)*y[x]) + (3 - 5*x)*x*D[y[x],x] + 2*(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 {2 c_2 \text {arctanh}\left (\sqrt {x}\right )-2 c_2 \sqrt {x}+c_1}{x} \end{align*}

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x**2*(2 - 2*x)*Derivative(y(x), (x, 2)) + x*(3 - 5*x)*Derivative(y(x), x) + (-x - 1)*y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

False