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1. Find the general solution of each differential equation. a) 1 dy 1 x dx y2 -2 b) (x-3)y = y c) y? dy = Inx dx x dx dr d) r = sin e dᎾ dy e) tan x“ = 2y² sec x dx 2. A curve for which e--dy. =1, passes through the point (0,-1). Find the equation of dx the curve. 3. Find the equation of the curve which passes through the point (1,1) and is defined by the differential equation yer dy Ee2* Show that the curve also passes through the dx point (2,2) and sketch the curve. 4. If the half life of a radioactive element that is decaying naturally is 500 years, find how many years it will be before the original mass of the element is reduced by 75%. 5. What constant interest rate is required if an initial deposit placed into an account that accrues interest compounded continuously is to double its value in six years? Note: Since interest is compounded continuously, the balance N(t) in the account at any time tis governed by the following differential equation: dN =kN dt