4.12.34 $3x^{2}y(x)y^{\prime }(x)+2xy(x{)}^2+1=0$

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

[[_homogeneous, `class G`], _rational, _Bernoulli]

Book solution method
The Bernoulli ODE

Mathematica ✓
cpu = 0.00776119 (sec), leaf count = 47

$$\{\{y(x)\to -\sqrt{\frac{c_1}{x^{4/3}}-\frac{2}{x}}\},\{y(x)\to \sqrt{\frac{c_1}{x^{4/3}}-\frac{2}{x}}\}\}$$

Maple ✓
cpu = 0.008 (sec), leaf count = 19

$$\{{\left(y\left(x\right)\right)}^2+2x^{-1}-\mathit{\_}\mathit{C}\mathit{1}{x}^{-\frac{4}{3}}=0\}$$ Mathematica raw input

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

Mathematica raw output

{{y[x] -> -Sqrt[-2/x + C[1]/x^(4/3)]}, {y[x] -> Sqrt[-2/x + C[1]/x^(4/3)]}}

Maple raw input

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

Maple raw output

y(x)^2+2/x-1/x^(4/3)*_C1 = 0