Someone deposits money in a bank account at a continuous rate of $5000$ per year, and the account earns interest at a continuous rate of $7\%$ per year. Is the differential equation for the balance $B$ in dollars, as a function of years, t $$\frac{dB}{dt}=5000+0.07B?$$
Or do I not need the $5000$? Since the $5000$ are not deposited initially... Should the equation be $$\frac{dB}{dt}t=0.07B$$ instead?