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11 Nov 2019
Suppose that we use Euler's method to approximate the solution to the differential equation dy / dx = x1 / y; y(0.5) = 2. Let f(x, y) = x1 / y. We let x0 = 0.5 and y0 = 2 and pick a step size h = 0.2. Euler's method is the the following algorithm. From xn and yn, our approximations to the solution of the differential equation at the nth stage: we find the next stage by computing Xn + 1 = xn + h, yn + 1 = yn + h middot f(xn, yn). Complete the following table: n xn yn The exact solution can also be found using separation of variables. It is y(x) = Thus the actual value of the function at the point x = 1.5 y( 1.5) =
Suppose that we use Euler's method to approximate the solution to the differential equation dy / dx = x1 / y; y(0.5) = 2. Let f(x, y) = x1 / y. We let x0 = 0.5 and y0 = 2 and pick a step size h = 0.2. Euler's method is the the following algorithm. From xn and yn, our approximations to the solution of the differential equation at the nth stage: we find the next stage by computing Xn + 1 = xn + h, yn + 1 = yn + h middot f(xn, yn). Complete the following table: n xn yn The exact solution can also be found using separation of variables. It is y(x) = Thus the actual value of the function at the point x = 1.5 y( 1.5) =
Jamar FerryLv2
10 Jan 2019