ODE
\[ x \left (x^2+1\right ) y'(x)=2 \left (1-2 x^2 y(x)\right ) \] ODE Classification
[_linear]
Book solution method
Linear ODE
Mathematica ✓
cpu = 0.16469 (sec), leaf count = 23
\[\left \{\left \{y(x)\to \frac {x^2+2 \log (x)+c_1}{\left (x^2+1\right )^2}\right \}\right \}\]
Maple ✓
cpu = 0.009 (sec), leaf count = 21
\[\left [y \left (x \right ) = \frac {x^{2}+2 \ln \left (x \right )+\textit {\_C1}}{\left (x^{2}+1\right )^{2}}\right ]\] Mathematica raw input
DSolve[x*(1 + x^2)*y'[x] == 2*(1 - 2*x^2*y[x]),y[x],x]
Mathematica raw output
{{y[x] -> (x^2 + C[1] + 2*Log[x])/(1 + x^2)^2}}
Maple raw input
dsolve(x*(x^2+1)*diff(y(x),x) = 2-4*x^2*y(x), y(x))
Maple raw output
[y(x) = (x^2+2*ln(x)+_C1)/(x^2+1)^2]