Question

if dy/dx=(y-1)/x^2 and f(1)=2. Use Euler's method with step delta x=0.1 to estimate f(1.2)

Answer 1

Well, do it. Start at ( 1 , 2 ) and move to ( 1.1 , ?? ). Then, move to ( 1.2 , ????)

Answer 2

I'm not sure how to use euler's method

Answer 3

Why on Earth are you assigned a problem to use Euler's Method?!

Euler's Method, essentially, is to move along the linear approximation of the non-given curve.

Start at ( 1 , 2 )
dy/dx = (2-1)/1^2 = 1/1 ==> 1 * 0.1 = 0.1
We end up at (1 + 0.1 , 2 + 0.1) ==> ( 1.1 , 2.1 )

Do it again.

Start at ( 1.1 , 2.1 )
dy/dx = (2.1-1)/1.1^2 = 1.1/1.21 = 0.9091 ==> 0.9091 * 0.1 = 0.09091
We end up at (1.1 + 0.1 , 2.1 + 0.09091) ==> ( 1.2 , 2.19091 )

More Exact answers are ( 1.1 , 2.0952 ) and ( 1.2 , 2.1814 ), so you can see that we have wandered off a bit. This is the nature of Euler's method with that massive step size!