ODE
\[ \left (x^2+1\right ) y'(x)=2 x (x-y(x)) \] ODE Classification
[_linear]
Book solution method
Linear ODE
Mathematica ✓
cpu = 0.00589057 (sec), leaf count = 25
\[\left \{\left \{y(x)\to \frac {3 c_1+2 x^3}{3 x^2+3}\right \}\right \}\]
Maple ✓
cpu = 0.006 (sec), leaf count = 23
\[ \left \{ y \left ( x \right ) ={\frac {2\,{x}^{3}+3\,{\it \_C1}}{3\,{x}^{2}+3}} \right \} \] Mathematica raw input
DSolve[(1 + x^2)*y'[x] == 2*x*(x - y[x]),y[x],x]
Mathematica raw output
{{y[x] -> (2*x^3 + 3*C[1])/(3 + 3*x^2)}}
Maple raw input
dsolve((x^2+1)*diff(y(x),x) = 2*x*(x-y(x)), y(x),'implicit')
Maple raw output
y(x) = (2*x^3+3*_C1)/(3*x^2+3)