Question

Suppose that we use Euler's method to approximate the solution to the differential equation dy/dx = x^5/y; y(0.4) = 7. Let f(x,y) = x^5/y. We let x0 = 0.4 and y0 = 7 and pick a step size h = 0.2. Euler's method is 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*f(xn,yn). Complete the following table. Your answers should be accurate to at least seven decimal places. n xn yn 0 0.4 7 1 2 3 4 5 The exact solution can also be found using separation of variables. It is y(x) = sqrt(x^6 - 49). Thus the actual value of the function at the point x = 1.4 is y(1.4) = sqrt(1.4^6 - 49).

          Suppose that we use Euler's method to approximate the solution to the differential equation dy/dx = x^5/y; y(0.4) = 7. Let f(x,y) = x^5/y. We let x0 = 0.4 and y0 = 7 and pick a step size h = 0.2. Euler's method is 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*f(xn,yn). Complete the following table. Your answers should be accurate to at least seven decimal places.

n   xn   yn
0   0.4   7
1   
2   
3   
4   
5   

The exact solution can also be found using separation of variables. It is y(x) = sqrt(x^6 - 49). Thus the actual value of the function at the point x = 1.4 is y(1.4) = sqrt(1.4^6 - 49).

Added by Nathan L.

Question

Please give Ace some feedback