ODE
\[ \left (x^2+1\right ) y'(x)=2 x (x-y(x)) \] ODE Classification
[_linear]
Book solution method
Linear ODE
Mathematica ✓
cpu = 0.172385 (sec), leaf count = 25
\[\left \{\left \{y(x)\to \frac {2 x^3+3 c_1}{3 x^2+3}\right \}\right \}\]
Maple ✓
cpu = 0.007 (sec), leaf count = 19
\[\left [y \left (x \right ) = \frac {\frac {2 x^{3}}{3}+\textit {\_C1}}{x^{2}+1}\right ]\] 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))
Maple raw output
[y(x) = (2/3*x^3+_C1)/(x^2+1)]