60.3.221 problem 1237

Internal problem ID [11217]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 2, linear second order
Problem number : 1237
Date solved : Wednesday, March 05, 2025 at 01:45:54 PM
CAS classification : [[_2nd_order, _missing_y]]

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

✓ Maple. Time used: 0.003 (sec). Leaf size: 20

ode:=(x^2-1)*diff(diff(y(x),x),x)+2*x*diff(y(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: 0.02 (sec). Leaf size: 26

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]
 

\[ y(x)\to \int _1^x\frac {c_1}{K[1]^2-1}dK[1]+c_2 \]

✓ Sympy. Time used: 0.262 (sec). Leaf size: 17

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

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