23.3.408 problem 412

Internal problem ID [6122]
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 : 412
Date solved : Tuesday, September 30, 2025 at 02:21:55 PM
CAS classification : [[_2nd_order, _exact, _linear, _homogeneous]]

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

✓ Maple. Time used: 0.001 (sec). Leaf size: 19

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

\[ y = \frac {c_1 +x^{a +1} c_2}{1+x} \]

✓ Mathematica. Time used: 0.054 (sec). Leaf size: 67

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

✗ Sympy

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

ValueError : Expected Expr or iterable but got None