23.3.358 problem 362

Internal problem ID [6072]
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 : 362
Date solved : Tuesday, September 30, 2025 at 02:21:00 PM
CAS classification : [[_2nd_order, _missing_y]]

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

✓ Maple. Time used: 0.001 (sec). Leaf size: 26

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

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

✓ Mathematica. Time used: 0.026 (sec). Leaf size: 36

ode=a - 2*x*D[y[x],x] + (1 - x^2)*D[y[x],{x,2}] == 0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \frac {1}{2} (a+c_1) \log (1-x)+\frac {1}{2} (a-c_1) \log (x+1)+c_2 \end{align*}

✓ Sympy. Time used: 0.345 (sec). Leaf size: 24

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

\[ y{\left (x \right )} = C_{1} + \frac {\left (- C_{2} + a\right ) \log {\left (x + 1 \right )}}{2} + \frac {\left (C_{2} + a\right ) \log {\left (x - 1 \right )}}{2} \]