4.6.39 $(x^2+1)y^{\prime }(x)=x(x^2+1)-xy(x)$

ODE
$$(x^2+1)y^{\prime }(x)=x(x^2+1)-xy(x)$$ ODE Classification

[_linear]

Book solution method
Linear ODE

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

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

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

$$\{y\left(x\right)=\frac{x^2}{3}+\frac{1}{3}+\mathit{\_}\mathit{C}\mathit{1}\frac{1}{\sqrt{x^2+1}}\}$$ 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