23.3.357 problem 361

Internal problem ID [6071]
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 : 361
Date solved : Tuesday, September 30, 2025 at 02:20:59 PM
CAS classification : [[_2nd_order, _missing_y]]

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

✓ Maple. Time used: 0.001 (sec). Leaf size: 20

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

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

✓ Mathematica. Time used: 0.01 (sec). Leaf size: 27

ode=-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} c_1 (\log (1-x)-\log (x+1))+c_2 \end{align*}

✓ Sympy. Time used: 0.149 (sec). Leaf size: 17

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

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