# Euler Method¶

For linear first ODE,

$\frac{dy}{dx} = f(x, y),$

we can discretize the equation using a step size :math:delta x cdot  so that the differential equation becomes

$\frac{y_{n+1} - y_n }{ \delta x } = f(x_n, y_n),$

which is also written as

(1)$y_{n+1} = y_n + \delta x \cdot f(x_n, y_n).$

Generally speaking, a simple iteraction will do the work.