What is the solution for (dP)/(dt)= 1/10 P(500-P) ?

The solution for (dP)/(dt)= 1/10 P(500-P) is P=(50)/(e^{-50t-c_{1)}-1}

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

(dP)/(dt)= 1/10 P(500-P)

\frac{d P}{d t} = \frac{1}{10} P (500 - P)

P = \frac{50}{e ^{- 50 t - c_{1}} - 1}

Solution steps

\frac{d P}{d t} = \frac{1}{10} P (500 - P)

Solve Bernoulli ODE:

P = \frac{50}{e ^{- 50 t - c_{1}} - 1}

P = \frac{50}{e ^{- 50 t - c_{1}} - 1}

\int sec^{2} (5 x) tan^{4} (5 x) d x

x \to 1 lim (\frac{x ^{2} - 4}{x - 1})

f (t) = e^{t + 7}

3 y

\frac{d}{d x} (\frac{1}{3 x ^{2}} - \frac{5}{2 x} + 8 x - 6)

What is the solution for (dP)/(dt)= 1/10 P(500-P) ?
The solution for (dP)/(dt)= 1/10 P(500-P) is P=(50)/(e^{-50t-c_{1)}-1}