##### 4.12.34 $$3 x^2 y(x) y'(x)+2 x y(x)^2+1=0$$

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

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

Book solution method
The Bernoulli ODE

Mathematica
cpu = 0.317327 (sec), leaf count = 47

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

Maple
cpu = 0.033 (sec), leaf count = 50

$\left [y \left (x \right ) = \frac {\sqrt {-x^{\frac {7}{3}} \left (2 x^{\frac {4}{3}}-x \textit {\_C1} \right )}}{x^{\frac {7}{3}}}, y \left (x \right ) = -\frac {\sqrt {-x^{\frac {7}{3}} \left (2 x^{\frac {4}{3}}-x \textit {\_C1} \right )}}{x^{\frac {7}{3}}}\right ]$ 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))

Maple raw output

[y(x) = 1/x^(7/3)*(-x^(7/3)*(2*x^(4/3)-x*_C1))^(1/2), y(x) = -1/x^(7/3)*(-x^(7/3
)*(2*x^(4/3)-x*_C1))^(1/2)]