1. Euler's method is a numerical method for generating a table of values (x i, y i) that approximate the solution of the differential equation y' = f(x,y) with boundary condition y(x o) = y o. The first entry in the table is the starting point (x o, y o.). Given the entry (x i, y i), then entry (x i+1, y i+1) is obtained using the formula x i+1 = x i +? x and y i+1 = y i +? x? f(x i, y i). Where h is the small value called step size.;Use Euler's method to estimate the value of y when x = 2.5 for the solution of the differential equation y' = x + 3y/x with the boundary condition y(1) = 1. Take? x = 0.1, the exact solution of this differential equation is y = 2x 3 - x 2. Compare your approximation values with the exact value.;2. Twin primes are two primes that differ by 2 (e.g., 3 and 5, 101 and 103). Write a program that outputs all twin primes less than 1000 and the total count to a data file.
Paper#70221 | Written in 18-Jul-2015Price : $57