Need help with Higher derivative Euler method

Hi

I am trying solve numerically the equation using the higher derivative Euler method with 3 terms:

y' = 2x +y

with y(0)=0

h = 0.1 and aiming to to estimate y(0.5)

Can anyone who is familiar with this method offer some help in formulating the terms?

I have worked out the following:

y' = 2x +y

y'' = 2

So, yi+1 ≈ yi + (0.1)(2)xi + (0.1)yi + (0.1)^2/2! (2)

Is this correct?

Re: Need help with Higher derivative Euler method

Hey zzizi.

Hint: When you are differentiating d/dx (2x + y) then you get y'' = d/dx (2x + y) = 2 + dy/dx = 2 + 2x + y.

Also what is your formula for updating y(x+h) given y(x) for your Euler Method update?