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 = 0.00776119 (sec), leaf count = 47

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

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

\[ \left \{ \left (y \relax (x ) \right ) ^{2}+2\,{x}^{-1}-{{\it \_C1}{x}^{-{\frac {4}{3}}}}=0 \right \} \] 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),'implicit')

Maple raw output

y(x)^2+2/x-1/x^(4/3)*_C1 = 0