(2 points) Suppose that we use Euler's method to approximate the
solution to the differential equation
dy/dx=(x^5/)y ;
y(0.3)=5.
Let f(x,y)=(x^5)/y
We let x0=0.3 and y0=5 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*f(xn,yn).
Complete the following table. Your answers should be accurate to
at least seven decimal places.
n
xn
yn
0
0.3
5
1
2
3
4
5
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=1.3
y(1.3)= .