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

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

[_linear]

Book solution method
Linear ODE

Mathematica
cpu = 0.00913295 (sec), leaf count = 27

\[\left \{\left \{y(x)\to \frac {c_1}{\sqrt {x^2+1}}+\frac {1}{3} \left (x^2+1\right )\right \}\right \}\]

Maple
cpu = 0.01 (sec), leaf count = 20

\[ \left \{ y \relax (x ) ={\frac {{x}^{2}}{3}}+{\frac {1}{3}}+{{\it \_C1}{\frac {1}{\sqrt {{x}^{2}+1}}}} \right \} \] Mathematica raw input

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

Mathematica raw output

{{y[x] -> (1 + x^2)/3 + C[1]/Sqrt[1 + x^2]}}

Maple raw input

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

Maple raw output

y(x) = 1/3*x^2+1/3+1/(x^2+1)^(1/2)*_C1