What is the solution for (dP)/(dt)=0.5(P)(1-P/(1000)) ?

The solution for (dP)/(dt)=0.5(P)(1-P/(1000)) is P=-(1000e^{0.5t+c_{1}})/(1-e^{0.5t+c_{1)}}

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(dP)/(dt)=0.5(P)(1-P/(1000))

\frac{d P}{d t} = 0.5 (P) (1 - \frac{P}{1000})

P = - \frac{1000 e ^{0.5 t + c_{1}}}{1 - e ^{0.5 t + c_{1}}}

Solution steps

\frac{d P}{d t} = 0.5 (P) (1 - \frac{P}{1000})

Solve separable ODE:

P = - \frac{1000 e ^{0.5 t + c_{1}}}{1 - e ^{0.5 t + c_{1}}}

P = - \frac{1000 e ^{0.5 t + c_{1}}}{1 - e ^{0.5 t + c_{1}}}

\frac{d y}{d x} = \frac{3 sec ( y )}{( x + 1 ) ^{2}}

f (x) = \frac{4 x}{( x ^{2} + 1 ) ^{2}}

n = 1 \sum \infty n (sin (nπ))

\frac{d}{d x} ((1 - x)^{2} (1 + x)^{3})

n = 1 \sum \infty \frac{3 n}{- 2 n + 5}

What is the solution for (dP)/(dt)=0.5(P)(1-P/(1000)) ?
The solution for (dP)/(dt)=0.5(P)(1-P/(1000)) is P=-(1000e^{0.5t+c_{1}})/(1-e^{0.5t+c_{1)}}