What is the solution for 6x^'=2000x-2x^2 ?

The solution for 6x^'=2000x-2x^2 is x=-(1000e^{(1000t+1000c_{1})/3})/(1-e^{(1000(c_{1)+t))/3}}

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6x^'=2000x-2x^2

6 x^{^{'}} = 2000 x - 2 x^{2}

x = - \frac{1000 e ^{\frac{1000 t + 1000 c _{1}}{3}}}{1 - e ^{\frac{1000 ( c _{1} + t )}{3}}}

Solution steps

6 x^{'} (t) = 2000 x - 2 x^{2}

Solve separable ODE:

x = - \frac{1000 e ^{\frac{1000 t + 1000 c _{1}}{3}}}{1 - e ^{\frac{1000 ( c _{1} + t )}{3}}}

x = - \frac{1000 e ^{\frac{1000 t + 1000 c _{1}}{3}}}{1 - e ^{\frac{1000 ( c _{1} + t )}{3}}}

\frac{d x}{d t} = 3 \cdot x

\frac{d y}{d x} = 28 + 16 x + 28 y + 16 x y

x^{4} y d x + 6 d y = 0

u, d H (x) - d x = u (x) (x)^{2} d x

y^{^{'}} = k (y + 2), y (0) = 5

What is the solution for 6x^'=2000x-2x^2 ?
The solution for 6x^'=2000x-2x^2 is x=-(1000e^{(1000t+1000c_{1})/3})/(1-e^{(1000(c_{1)+t))/3}}