(a) Solve the differential equation dy/dx 4/√x + 6x² given the condition, y(4) = 3.
(b) The population, N, of a small country is currently 5 million. It is expected that this population will grow according to the differential equation.
dN/dt = 0.015N
where t is measured in years.
Solve this equation to express N in terms of t and hence predict how many years it will take for the population to double. Give your answer to one decimal place.