16 a Use Euler's method with step length 0.25 to sketch the solution in 0

a Use Euler's method with step length 0.25 to sketch the solution in 0 < x < 10 to + where y = I when x = 0. b Hence estimate, to one decimal place, the minimum value of y on this curve. dy Consider the differential equation = eY-x with the initial condition a Use Euler's method with step length 0.1 to estimate the value of y(2). b Solve the equation exactly to find the error in your estimate in part a. c How could you decrease the error in your estimate? The growth rate of a population of ilsects depends on its current size but also varies according to the dN = o.2N 1+2sin Itt time of year. This can be modelled by the differential equation , where N dt 6 thousand is the population size and t is the time in months since the measurements began. The initial population is 2000. Solve the differential equation to find the size of the population at time t. dy _ 3y Two variables satisfy the differential equation When x = 1, 2. CLY X2 a Use Euler's method with step length 0.1 to find an approximate value of y when x = 1.3. Give your answer to two decimal places. b Solve the differential equation.