17. dP/dt=P-P^2 by separable method.

To solve the differential equation by separable method, we need to separate the variables and on opposite sides of the equation and integrate both sides.

Starting with the given differential equation:

We can divide both sides by to obtain:

Now we can integrate both sides with respect to their respective variables:

where is a constant determined by the values of the constants of integration and .

Simplifying the last equation, we get:

where is a constant determined by the initial conditions.

Therefore, the general solution to the given differential equation is:

where is a constant determined by the initial conditions.