85.41.3 problem 2 (b)

Internal problem ID [22769]
Book : Applied Differential Equations. By Murray R. Spiegel. 3rd edition. 1980. Pearson. ISBN 978-0130400970
Section : Chapter 4. Linear differential equations. C Exercises at page 178
Problem number : 2 (b)
Date solved : Thursday, October 02, 2025 at 09:14:28 PM
CAS classification : [_Gegenbauer]

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

✓ Maple. Time used: 0.006 (sec). Leaf size: 38

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

\[ y = \frac {\left (3 c_1 -1\right ) x \ln \left (x -1\right )}{6}+\frac {\left (-1-3 c_1 \right ) x \ln \left (x +1\right )}{6}+\frac {\left (18 c_2 +11\right ) x}{18}+c_1 \]

✓ Mathematica. Time used: 0.039 (sec). Leaf size: 46

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

\begin{align*} y(x)&\to \frac {1}{6} (6 c_1 x-(x+3 c_2 x) \log (1-x)+(-1+3 c_2) x \log (x+1)-6 c_2) \end{align*}

✗ Sympy

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

NotImplementedError : The given ODE Derivative(y(x), x) - (-x**2*Derivative(y(x), (x, 2)) - x + 2*y(