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?