Verify that the indicated family of functions is a solution to the given differential equation.
dP/dt=P(1-P); P=(c1*e^t)/(1+c1*e^t)
Do I take the derivative of P first? If so do I just ignore the constants? Thanks for the help.
Verify that the indicated family of functions is a solution to the given differential equation.
dP/dt=P(1-P); P=(c1*e^t)/(1+c1*e^t)
Do I take the derivative of P first? If so do I just ignore the constants? Thanks for the help.
Sure.
$\displaystyle \frac{dP}{dt} = \frac{c e^t}{\left(1 + c e^t \right)^2} $
$\displaystyle P(1-P) = \frac{c e^t}{1 + c e^t} \left( 1 - \frac{c e^t}{1 + c e^t}\right) = \frac{c e^t}{1 + c e^t} \frac{1}{1 + c e^t} = \frac{c e^t}{\left(1 + c e^t \right)^2}$
see - the same.