Find general solutions for 18:

18. x2 =1-x-+ 2 X 2 2 32. Find a general solution and any singular solutions of the differential equation dy/dx = yvy2 - 1. Determine the points (a, b) in the plane for which the initial value prob- lem y = y vy2 - 1, y(a) = b has (a) no solution, (b) a unique solution, (c) infinitely many solutions.36. (Radiocarbon dating) Carbon taken from a purported relic of the time of Christ contained 4.6 x 1010 atoms of "(I per gram. Carbon extracted from a present-day specimen of the same substance contained 5.0 x 1010 atoms of 14IC per gram. Compute the approximate age of the relic. What is your opinion as to its authenticity? 37. (Continuously compounded interest) Upon the birth of their rst child, a couple deposited $5000 in an account that pays 8% interest compounded continuously. The in- terest payments are allowed to accumulate. How much will the account contain on the child's eighteenth birth- day? 39. (Drug elimination) Suppose that sodium pentobarbital is used to anesthetize a dog. The dog is anesthetized when its bloodstream contains at least 45 milligrams (mg) of sodium pentobarbitol per kilogram of the dog's body weight. Suppose also that sodium pentobarbitol is elim- inated exponentially from the dog's bloodstream, with a half-life of 5 h. What single dose should be administered in order to anesthetize a 50-kg dog for l h