What is the solution for dp=(3p-p^2-9/4)dt ?

The solution for dp=(3p-p^2-9/4)dt is t= 2/(2p-3)+c_{1}

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dp=(3p-p^2-9/4)dt

d p = (3 p - p^{2} - \frac{9}{4}) d t

t = \frac{2}{2 p - 3} + c_{1}

Solution steps

d p = (3 p - p^{2} - \frac{9}{4}) d t

Let

t

be the dependent variable. Divide by

d p

1 = (3 p - p^{2} - \frac{9}{4}) \frac{d t}{d p}

Substitute

\frac{d t}{d p}

with

t^{'} (p)

1 = (3 p - p^{2} - \frac{9}{4}) t^{^{'}} (p)

Isolate

t^{'} (p) : t^{'} (p) = \frac{4}{12 p - 4 p ^{2} - 9}

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

then

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

t = \int \frac{4}{12 p - 4 p ^{2} - 9} d p

\int \frac{4}{12 p - 4 p ^{2} - 9} d p = \frac{2}{2 p - 3} + c_{1}

t = \frac{2}{2 p - 3} + c_{1}

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What is the solution for dp=(3p-p^2-9/4)dt ?
The solution for dp=(3p-p^2-9/4)dt is t= 2/(2p-3)+c_{1}