What is the solution for y^'=y-(y^2)/3 ?

The solution for y^'=y-(y^2)/3 is y=-(3e^{t+c_{1}})/(1-e^{t+c_{1)}}

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y^'=y-(y^2)/3

y^{^{'}} = y - \frac{y ^{2}}{3}

y = - \frac{3 e ^{t + c_{1}}}{1 - e ^{t + c_{1}}}

Solution steps

y^{'} (t) = y - \frac{y ^{2}}{3}

Solve separable ODE:

y = - \frac{3 e ^{t + c_{1}}}{1 - e ^{t + c_{1}}}

y = - \frac{3 e ^{t + c_{1}}}{1 - e ^{t + c_{1}}}

\frac{d y}{d x} = \frac{1 + 2 y}{4 - x ^{2}}

\frac{d y}{d x} = \frac{x ^{5}}{y}

y^{^{'}} = \frac{y ^{2}}{x} - \frac{1}{x}

\frac{d y}{d x} = - \frac{x}{y}, y (1) = 2

x \frac{d y}{d x} + y = y^{- 3}

What is the solution for y^'=y-(y^2)/3 ?
The solution for y^'=y-(y^2)/3 is y=-(3e^{t+c_{1}})/(1-e^{t+c_{1)}}