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To solve the DE

[tex]y(t) + \frac{dy(t)}{dt} = 1[/tex] where [tex]y(t) = 0[/tex],

using the Euler (forward) method, we can approximate to:

[tex]y[n+1] = T + (1-T)y[n] [/tex] where [tex]T[/tex] is step size and [tex]y[0] = 0[/tex].

I have no idea how this result is obtained, the only thing they say is that in general for

[tex]\frac{dx_1}{dt} = \frac{x_1[n+1] - x_1[n]}{T}[/tex] for [tex]t = nT[/tex].

Can anyone please help me understand how they arrived at the solution for [tex]y[n+1][/tex]? Thanks!