54.3.222 problem 1238

Internal problem ID [12517]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 2, linear second order
Problem number : 1238
Date solved : Wednesday, October 01, 2025 at 01:46:16 AM
CAS classification : [[_2nd_order, _missing_y]]

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

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

ode:=(x^2-1)*diff(diff(y(x),x),x)+2*x*diff(y(x),x)-a = 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: 10.315 (sec). Leaf size: 31

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 \int _1^x\frac {c_1+a K[1]}{K[1]^2-1}dK[1]+c_2 \end{align*}

✓ Sympy. Time used: 0.359 (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) + (x**2 - 1)*Derivative(y(x), (x, 2)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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