Final answer:
To find the solution to the given differential equation P dP/dt = 1 with the initial condition P(0) = 2, use separation of variables. Separate the variables and integrate both sides. Substitute the initial condition and solve for the constant of integration.
Step-by-step explanation:
To find the solution to the given differential equation P dP/dt = 1 with the initial condition P(0) = 2, we can use separation of variables. Separate the variables and integrate both sides: ∫P dP = ∫1 dt. On the left side, integrate P with respect to P, and on the right side, integrate 1 with respect to t. This gives us: (P^2)/2 = t + C, where C is the constant of integration.
Substitute the initial condition P(0) = 2 into the equation to solve for C. When t = 0, (2^2)/2 = 0 + C, so C = 2. Therefore, the solution to the differential equation with the given initial condition is: (P^2)/2 = t + 2.