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Popular >

(dp)/(p-p^2)=dt

Solution

\frac{d p}{p - p ^{2}} = d t

Solution

t = ln (p) - ln (p - 1) + c_{1}

Solution steps

\frac{d p}{p - p ^{2}} = d t

Let

t

be the dependent variable. Divide by

d p

:

\frac{1}{p - p ^{2}} = \frac{d t}{d p}

Substitute

\frac{d t}{d p}

with

t^{'} (p)

\frac{1}{p - p ^{2}} = t^{^{'}} (p)

Isolate

t^{'} (p) : t^{'} (p) = \frac{1}{p - p ^{2}}

If

f^{^{'}} (x) = g (x)

then

f (x) = \int g (x) d x

t = \int \frac{1}{p - p ^{2}} d p

\int \frac{1}{p - p ^{2}} d p = ln (p) - ln (p - 1) + c_{1}

t = ln (p) - ln (p - 1) + c_{1}

Popular Examples

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

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\int \frac{1}{e ^{x} + 3} d x

derivative of y=sin(x)ln(2x)derivative of

y = sin (x) ln (2 x)

Frequently Asked Questions (FAQ)

What is the solution for (dp)/(p-p^2)=dt ?
The solution for (dp)/(p-p^2)=dt is t=ln(p)-ln(p-1)+c_{1}