Question

Use Euler’s method with two steps to estimate y(1) if y(x) is the solution to dy dx = x + y, y(0) = 1. Write your answer in the form a b where a and b are integers.

Answer 1

1.5

Explanation:

The Euler's method is a common approximation method for the solution of differential equations. It can be used to obtain an approximate value of a given function. The Euler's formula is:

`y_(n) = y_(n-1) + hF(_{x_(n-1),y_(n-1)})`

Therefore, n =1 will give:

`y_(1) = y_(0) + hF(x_(0),y_(0))`

h is the step size and it is equivalent to
`(x_(1)-x_(2))/(2) = (1-0)/(2)=(1)/(2)`

`F(x_(0),y_(0)) = x_(0) + y_(0) = 0 + 1 = 1`

`y_(1) = 1 + (0.5)(0+1) = 1 + (0.5)(1) = 1 + 0.5 = 1.5`