ODE
\[ x \left (1-x^2\right ) y'(x)=\left (x^2-x+1\right ) y(x) \] ODE Classification
[_separable]
Book solution method
Separable ODE, Neither variable missing
Mathematica ✓
cpu = 0.180685 (sec), leaf count = 25
\[\left \{\left \{y(x)\to \frac {c_1 x}{(x+1) \sqrt {1-x^2}}\right \}\right \}\]
Maple ✓
cpu = 0.013 (sec), leaf count = 17
\[\left [y \left (x \right ) = \frac {\textit {\_C1} x}{\left (1+x \right )^{\frac {3}{2}} \sqrt {x -1}}\right ]\] Mathematica raw input
DSolve[x*(1 - x^2)*y'[x] == (1 - x + x^2)*y[x],y[x],x]
Mathematica raw output
{{y[x] -> (x*C[1])/((1 + x)*Sqrt[1 - x^2])}}
Maple raw input
dsolve(x*(-x^2+1)*diff(y(x),x) = (x^2-x+1)*y(x), y(x))
Maple raw output
[y(x) = _C1*x/(1+x)^(3/2)/(x-1)^(1/2)]