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 = 0.245367 (sec), leaf count = 37
\[\left \{\left \{y(x)\to -\sqrt {x^3+c_1 x+1}\right \},\left \{y(x)\to \sqrt {x^3+c_1 x+1}\right \}\right \}\]
Maple ✓
cpu = 0.021 (sec), leaf count = 29
\[\left [y \left (x \right ) = \sqrt {x^{3}+x \textit {\_C1} +1}, y \left (x \right ) = -\sqrt {x^{3}+x \textit {\_C1} +1}\right ]\] 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))
Maple raw output
[y(x) = (x^3+_C1*x+1)^(1/2), y(x) = -(x^3+_C1*x+1)^(1/2)]