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 = 0.011488 (sec), leaf count = 25
\[\left \{\left \{y(x)\to \frac {c_1 x}{(x+1) \sqrt {1-x^2}}\right \}\right \}\]
Maple ✓
cpu = 0.02 (sec), leaf count = 17
\[ \left \{ y \left ( x \right ) ={{\it \_C1}\,x{\frac {1}{\sqrt {-1+x}}} \left ( 1+x \right ) ^{-{\frac {3}{2}}}} \right \} \] 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),'implicit')
Maple raw output
y(x) = _C1/(-1+x)^(1/2)/(1+x)^(3/2)*x