Find the solution of the differential equation that satisfies the given initial condition. (dP)/(dt)

Step-by-step explanation:

Given

Required

The solution

We have:

Split

Divide both sides by

Multiply both sides by dt

Integrate

Rewrite as:

Integrate the left hand side

Integrate the right hand side

---- (1)

To solve for c, we first make c the subject

means

So:

So, we have:

Divide through by 2

Square both sides

graph b

step-by-step explanation:

one solution- graph a (clear intercepting point.)

no solution- graph b (they're parallel, there will never be a point of interception.)

infinite solutions- graph c (all points intercept.)