What is the solution for (dx)/(dt)=30-11x+x^2 ?

The solution for (dx)/(dt)=30-11x+x^2 is x=-(5e^{t+c_{1}})/(1-e^{t+c_{1)}}+6/(1-e^{t+c_{1)}}

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(dx)/(dt)=30-11x+x^2

\frac{d x}{d t} = 30 - 11 x + x^{2}

x = - \frac{5 e ^{t + c_{1}}}{1 - e ^{t + c_{1}}} + \frac{6}{1 - e ^{t + c_{1}}}

Solution steps

\frac{d x}{d t} = 30 - 11 x + x^{2}

Solve separable ODE:

x = - \frac{5 e ^{t + c_{1}}}{1 - e ^{t + c_{1}}} + \frac{6}{1 - e ^{t + c_{1}}}

x = - \frac{5 e ^{t + c_{1}}}{1 - e ^{t + c_{1}}} + \frac{6}{1 - e ^{t + c_{1}}}

\frac{d}{d x} (x y) = \frac{d}{d x} (x + y)

\frac{d}{d x} ((x) y) = (y) x

\frac{d}{d x} (z (x) \cdot e^{2 x}) = e^{2 x}

e^{y} \cdot d y - 2 x \cdot d x = 0

\frac{d y}{d t} + 24 \cdot 1 0^{- 3} y = 384 \cdot 1 0^{- 3}

What is the solution for (dx)/(dt)=30-11x+x^2 ?
The solution for (dx)/(dt)=30-11x+x^2 is x=-(5e^{t+c_{1}})/(1-e^{t+c_{1)}}+6/(1-e^{t+c_{1)}}