What is the solution for (dy)/(dx)=y^2-y-2 ?

The solution for (dy)/(dx)=y^2-y-2 is y=-(2e^{-3x-3c_{1}})/(1-e^{-3(x+c_{1))}}-1/(1-e^{-3(x+c_{1))}}

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(dy)/(dx)=y^2-y-2

\frac{d y}{d x} = y^{2} - y - 2

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

Solution steps

\frac{d y}{d x} = y^{2} - y - 2

Solve separable ODE:

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

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

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