##### 4.5.43 $$2 x y'(x)=y(x) \left (-6 y(x)^2+x+1\right )$$

ODE
$2 x y'(x)=y(x) \left (-6 y(x)^2+x+1\right )$ ODE Classiﬁcation

[_rational, _Bernoulli]

Book solution method
The Bernoulli ODE

Mathematica
cpu = 0.253894 (sec), leaf count = 60

$\left \{\left \{y(x)\to -\frac {e^{x/2} \sqrt {x}}{\sqrt {6 e^x+c_1}}\right \},\left \{y(x)\to \frac {e^{x/2} \sqrt {x}}{\sqrt {6 e^x+c_1}}\right \}\right \}$

Maple
cpu = 0.026 (sec), leaf count = 54

$\left [y \left (x \right ) = \frac {\sqrt {\left (\textit {\_C1} \,{\mathrm e}^{-x}+6\right ) x}}{\textit {\_C1} \,{\mathrm e}^{-x}+6}, y \left (x \right ) = -\frac {\sqrt {\left (\textit {\_C1} \,{\mathrm e}^{-x}+6\right ) x}}{\textit {\_C1} \,{\mathrm e}^{-x}+6}\right ]$ Mathematica raw input

DSolve[2*x*y'[x] == y[x]*(1 + x - 6*y[x]^2),y[x],x]

Mathematica raw output

{{y[x] -> -((E^(x/2)*Sqrt[x])/Sqrt[6*E^x + C[1]])}, {y[x] -> (E^(x/2)*Sqrt[x])/S
qrt[6*E^x + C[1]]}}

Maple raw input

dsolve(2*x*diff(y(x),x) = (1+x-6*y(x)^2)*y(x), y(x))

Maple raw output

[y(x) = 1/(_C1*exp(-x)+6)*((_C1*exp(-x)+6)*x)^(1/2), y(x) = -1/(_C1*exp(-x)+6)*(
(_C1*exp(-x)+6)*x)^(1/2)]