Suppose that we use Euler's method to approximate the solution to the differential equation $$\frac{dy}{dx}= \frac{x^1}{y};\qquad y( 0.1) = 6.$$ Let $f(x,y) = x^1/y.$
We let $x_0 = 0.1$ and $y_0 = 6$ and pick a step size $h=0.2 .$ Euler's method is the the following algorithm. From $x_n$ and $y_n ,$ our approximations to the solution of the differential equation at the nth stage, we find the next stage by computing $$x_{n+1} = x_n +h,\qquad y_{n+1} = y_n + h\cdot f(x_n,y_n).$$ Complete the following table. Your answers should be accurate to at least seven decimal places.

$n$	$x_n$	$y_n$
$0$	$0.1$	$6$
$1$
$2$
$3$
$4$
$5$

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 $x=1.1$
$y(1.1 ) =$ .