Question

Please help me solve the following differential equation by separation of variables.

dP/dt=P-(P^2)

Answer 1

\[\frac{ dP }{ dt }=P-P^2\]

Answer 2

i havent done differential equations but
\[\frac{dP}{P-P^2}=dt\\ \int \frac{dP}{P-P^2}=\int dt\\ \ln\frac{P}{P+1}+c_1=t+c_2\\P+\frac{1}{P} =e^{k-t}\]

Answer 3

\[\frac{ 1 }{ p-p ^{2} }=\frac{ 1 }{ p \left( 1-p \right) }=\frac{ 1 }{p }+\frac{ 1 }{1-p }\]
now you can integrate