1. The problem statement, all variables and given/known data A college student wants to start a new savings account with an initial balance of $0. He plans to save money at a continuous rate of $700 per month. Additionally, every month he plans to increase this rate by $7. (Such that for example in month 3 he is saving at rate $721 per month.) Also, he found a bank account that pays continuously compounded interest at a rate of 9% per year. Estimate how long it will take the college to save $500,000. Note that you will need to set up and solve a DE, and then you'll need to plot the solution to make the final estimate. 2. Relevant equations 3. The attempt at a solution Setting up the differential equation is the problem for me. Let S = the amount of money in his savings account let t = time (in months) dS/dt = (0.09/12)(S + 7t) I divided 0.09(bank interest) by 12 b/c of the college student adding in money every month I multiplied the bank's interest per month by (S+7t) because the interest is acted upon the amount of money in the savings account. When I solve for the general equation by using an integrating factor, I can't fulfill the initial conditions in the final general solution. What's wrong with my differential equation? Thanks!