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 = 0.0109751 (sec), leaf count = 60

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

Maple
cpu = 0.008 (sec), leaf count = 23

\[ \left \{ -6\,{x}^{-1}-{\frac {{{\rm e}^{-x}}{\it \_C1}}{x}}+ \left (y \relax (x ) \right ) ^{-2}=0 \right \} \] 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),'implicit')

Maple raw output

-6/x-1/x*exp(-x)*_C1+1/y(x)^2 = 0