If the resistance of the car is constant f, the instantaneous acceleration of the car is a=(F-f)/m=(P/v-f)/m=(P-fv)/(mv).

Combining dv/dt=a, the following differential equations are listed:

dvdt=(P-fv)/(mv)=-f/m+P/(mv)

Since the subject can solve this differential equation, it must be an implicit function expression, which should be t=t(v).

But the subject sees the expression clearly by himself. Is this Bernoulli equation?

Stop joking. The form of Bernoulli equation is dx/dt = p (t) x+q (t) x β (β ≠ 0, 1).

You can only use this form, and there is this question-where is the V in F/M? You can't do this at all, and you can't do it. It can only be a method of separating variables. T=t(v), not v=v(t).

The problem mainly knows that not every differential equation can give an explicit function expression, which is the case.

You're welcome. Welcome to communicate if you don't understand.