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

ODE
\[ \left (x^2+1\right ) y'(x)=2 x \left (x^2+1\right )^2+2 x y(x) \] ODE Classification

[_linear]

Book solution method
Linear ODE

Mathematica
cpu = 0.00624031 (sec), leaf count = 17

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

Maple
cpu = 0.007 (sec), leaf count = 15

\[ \left \{ y \relax (x ) = \left ({x}^{2}+{\it \_C1} \right ) \left ({x}^{2}+1 \right ) \right \} \] Mathematica raw input

DSolve[(1 + x^2)*y'[x] == 2*x*(1 + x^2)^2 + 2*x*y[x],y[x],x]

Mathematica raw output

{{y[x] -> (1 + x^2)*(x^2 + C[1])}}

Maple raw input

dsolve((x^2+1)*diff(y(x),x) = 2*x*(x^2+1)^2+2*x*y(x), y(x),'implicit')

Maple raw output

y(x) = (x^2+_C1)*(x^2+1)