4.6.42 \(\left (x^2+1\right ) y'(x)=2 x (x-y(x))\)

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

\[ \left \{ y \relax (x ) ={\frac {2\,{x}^{3}+3\,{\it \_C1}}{3\,{x}^{2}+3}} \right \} \] 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)