4.12.26 $(x^2+1)y(x)y^{\prime }(x)+x(1-y(x{)}^2)=0$

ODE
$$(x^2+1)y(x)y^{\prime }(x)+x(1-y(x{)}^2)=0$$ ODE Classification

[_separable]

Book solution method
Separable ODE, Neither variable missing

Mathematica ✓
cpu = 0.0160068 (sec), leaf count = 47

$$\{\{y(x)\to -\sqrt{e^{2c_1}(x^2+1)+1}\},\{y(x)\to \sqrt{e^{2c_1}(x^2+1)+1}\}\}$$

Maple ✓
cpu = 0.007 (sec), leaf count = 18

$$\{-\mathit{\_}\mathit{C}\mathit{1}{x}^2+{\left(y\left(x\right)\right)}^2-\mathit{\_}\mathit{C}\mathit{1}-1=0\}$$ Mathematica raw input

DSolve[x*(1 - y[x]^2) + (1 + x^2)*y[x]*y'[x] == 0,y[x],x]

Mathematica raw output

{{y[x] -> -Sqrt[1 + E^(2*C[1])*(1 + x^2)]}, {y[x] -> Sqrt[1 + E^(2*C[1])*(1 + x^
2)]}}

Maple raw input

dsolve((x^2+1)*y(x)*diff(y(x),x)+x*(1-y(x)^2) = 0, y(x),'implicit')

Maple raw output

-_C1*x^2+y(x)^2-_C1-1 = 0