Urgent! Need help with Differential Compound Interest Rate Problem!

I've been thinking about this problem for an hour and it's due in 2 hours!

Find the amount in a savings account after one year if the initial balance in the account was $1000, the interest is paid continuously into the account at a nominal rate of 10% per annum(compounded continuously), and the account is being continuously depleted(by taxes say) at the rate of y^2 per million dollars per year. The balance in the account after t years is given by y=y(t). How large can the account grow? How long will it take the account to grow to half of this maximum balance?

I've worked out that dy/dt=0.1y-y^2/10^6
y=y^2/20-y^3/(3*10^6)

I dont know what to do from here since I'm not really sure how to deal with the ys in the function equation above.
ANY HELP will be greatly appreciated!!!!!!!!!!
Thank you in advance!