# Euler forward equation

by ChickenChakuro
Tags: equation, euler, forward
 P: 32 Hi all, I'm having trouble understanding a basic concept introduced in one of my lectures. It says that: To solve the DE $$y(t) + \frac{dy(t)}{dt} = 1$$ where $$y(t) = 0$$, using the Euler (forward) method, we can approximate to: $$y[n+1] = T + (1-T)y[n]$$ where $$T$$ is step size and $$y[0] = 0$$. I have no idea how this result is obtained, the only thing they say is that in general for $$\frac{dx_1}{dt} = \frac{x_1[n+1] - x_1[n]}{T}$$ for $$t = nT$$. Can anyone please help me understand how they arrived at the solution for $$y[n+1]$$? Thanks!