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