4.11.42 \(-2 x^3+2 x y(x) y'(x)-y(x)^2+1=0\)

ODE
\[ -2 x^3+2 x y(x) y'(x)-y(x)^2+1=0 \] ODE Classification

[_rational, _Bernoulli]

Book solution method
The Bernoulli ODE

Mathematica
cpu = 0.00970668 (sec), leaf count = 37

\[\left \{\left \{y(x)\to -\sqrt {c_1 x+x^3+1}\right \},\left \{y(x)\to \sqrt {c_1 x+x^3+1}\right \}\right \}\]

Maple
cpu = 0.012 (sec), leaf count = 18

\[ \left \{ -{x}^{3}-{\it \_C1}\,x+ \left (y \relax (x ) \right ) ^{2}-1=0 \right \} \] Mathematica raw input

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

Mathematica raw output

{{y[x] -> -Sqrt[1 + x^3 + x*C[1]]}, {y[x] -> Sqrt[1 + x^3 + x*C[1]]}}

Maple raw input

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

Maple raw output

-x^3-_C1*x+y(x)^2-1 = 0