ODE
\[ x \left (x^2+1\right ) y''(x)-2 \left (1-x^2\right ) y'(x)-2 x y(x)=0 \] ODE Classification
[[_2nd_order, _exact, _linear, _homogeneous]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.168785 (sec), leaf count = 26
\[\left \{\left \{y(x)\to \frac {c_2 x^3+3 c_1}{3 x^2+3}\right \}\right \}\]
Maple ✓
cpu = 0.048 (sec), leaf count = 26
\[\left [y \left (x \right ) = \frac {\textit {\_C1}}{x^{2}+1}+\frac {\textit {\_C2} \,x^{3}}{x^{2}+1}\right ]\] Mathematica raw input
DSolve[-2*x*y[x] - 2*(1 - x^2)*y'[x] + x*(1 + x^2)*y''[x] == 0,y[x],x]
Mathematica raw output
{{y[x] -> (3*C[1] + x^3*C[2])/(3 + 3*x^2)}}
Maple raw input
dsolve(x*(x^2+1)*diff(diff(y(x),x),x)-2*(-x^2+1)*diff(y(x),x)-2*x*y(x) = 0, y(x))
Maple raw output
[y(x) = _C1/(x^2+1)+_C2/(x^2+1)*x^3]