##### 4.12.6 $$-3 x^2+2 (x+1) y(x) y'(x)+y(x)^2+2 x=0$$

ODE
$-3 x^2+2 (x+1) y(x) y'(x)+y(x)^2+2 x=0$ ODE Classiﬁcation

[_exact, _rational, _Bernoulli]

Book solution method
Exact equation

Mathematica
cpu = 0.350999 (sec), leaf count = 56

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

Maple
cpu = 0.017 (sec), leaf count = 52

$\left [y \left (x \right ) = \frac {\sqrt {\left (x +1\right ) \left (x^{3}-x^{2}+\textit {\_C1} \right )}}{x +1}, y \left (x \right ) = -\frac {\sqrt {\left (x +1\right ) \left (x^{3}-x^{2}+\textit {\_C1} \right )}}{x +1}\right ]$ Mathematica raw input

DSolve[2*x - 3*x^2 + y[x]^2 + 2*(1 + x)*y[x]*y'[x] == 0,y[x],x]

Mathematica raw output

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

Maple raw input

dsolve(2*(x+1)*y(x)*diff(y(x),x)+2*x-3*x^2+y(x)^2 = 0, y(x))

Maple raw output

[y(x) = 1/(x+1)*((x+1)*(x^3-x^2+_C1))^(1/2), y(x) = -1/(x+1)*((x+1)*(x^3-x^2+_C1
))^(1/2)]