First graded homework (due 9/8)

For maximal credit, full working must be shown.
  1. (3 points.) At time  t  (in years), the price of a gallon of gas is $y(t) . If
    10y' = y ,
    how long does it take for the price to double? Give your answer rounded to the nearest whole number of years.

  2. (4 points.) Solve the initial value problem
    y' + y = et
    with  y(0) = 1 .

  3. (3 points.) Give an implicit solution to the initial value problem
    y'(x) = ( 1 + 4x3) / ( 1 + 4y)
    with  y(1) = 3 .