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

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 = 0.00718074 (sec), leaf count = 23

\[\left \{\left \{y(x)\to \frac {c_1+x^2+2 \log (x)}{\left (x^2+1\right )^2}\right \}\right \}\]

Maple
cpu = 0.01 (sec), leaf count = 21

\[ \left \{ y \relax (x ) ={\frac {{x}^{2}+2\,\ln \relax (x ) +{\it \_C1}}{ \left ({x}^{2}+1 \right ) ^{2}}} \right \} \] 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),'implicit')

Maple raw output

y(x) = (x^2+2*ln(x)+_C1)/(x^2+1)^2