What is the solution for 3xy^'=y^2-y-2 ?

The solution for 3xy^'=y^2-y-2 is y=-(2e^{-3c_{1}})/(x-e^{-3c_{1)}}-x/(x-e^{-3c_{1)}}

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3xy^'=y^2-y-2

3 x y^{^{'}} = y^{2} - y - 2

y = - \frac{2 e ^{- 3 c_{1}}}{x - e ^{- 3 c_{1}}} - \frac{x}{x - e ^{- 3 c_{1}}}

Solution steps

3 x y^{'} (x) = y^{2} - y - 2

Solve separable ODE:

y = - \frac{2 e ^{- 3 c_{1}}}{x - e ^{- 3 c_{1}}} - \frac{x}{x - e ^{- 3 c_{1}}}

y = - \frac{2 e ^{- 3 c_{1}}}{x - e ^{- 3 c_{1}}} - \frac{x}{x - e ^{- 3 c_{1}}}

f (x) = ln (3 x)

\int \frac{1}{( 4 - x ^{2} )} d x

\int (1 - x)^{\frac{1}{2}} d x

\int 9 x (9 - x^{- 4}) d x

x \to 3 - lim (\frac{x - 3}{x ^{2} - 9})

What is the solution for 3xy^'=y^2-y-2 ?
The solution for 3xy^'=y^2-y-2 is y=-(2e^{-3c_{1}})/(x-e^{-3c_{1)}}-x/(x-e^{-3c_{1)}}