4.12.6 $-3x^2+2(x+1)y(x)y^{\prime }(x)+y(x{)}^2+2x=0$

ODE
$$-3x^2+2(x+1)y(x)y^{\prime }(x)+y(x{)}^2+2x=0$$ ODE Classification

[_exact, _rational, _Bernoulli]

Book solution method
Exact equation

Mathematica ✓
cpu = 0.0136598 (sec), leaf count = 56

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

Maple ✓
cpu = 0.009 (sec), leaf count = 26

$$\{{\left(y\left(x\right)\right)}^2+\frac{-x^3+x^2-\mathit{\_}\mathit{C}\mathit{1}}{1+x}=0\}$$ 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*(1+x)*y(x)*diff(y(x),x)+2*x-3*x^2+y(x)^2 = 0, y(x),'implicit')

Maple raw output

y(x)^2+(-x^3+x^2-_C1)/(1+x) = 0